Фейгин Борис Львович

доктор физико-математических наук

• Факультет математики | Кафедра геометрии и топологии: профессор

Образование, учёные степени

Доктор наук: Институт теоретической физики им. Л.Д. Ландау РАН (год защиты: 1996, специальность: 01.00.00 Физико-математические науки)
Кандидат наук: Санкт-Петербургское отделение математического института им. В.А. Стеклова РАН (год защиты: 1983, специальность: 01.00.00 Физико-математические науки)
Аспирантура: Ярославский государственный университет (год окончания: 1979, специальность: Математика)
Специалитет: Московский государственный университет им. М.В. Ломоносова (год окончания: 1974, специальность: Математика)

Трудовая деятельность

2008 - настоящее время
факультет математики Государственного университета - Высшая школа экономики
профессор кафедры геометрии и топологии

1997 - настоящее время
Член редколлегии журнала "Функциональный анализ и его приложения"

1992 - настоящее время
Институт теоретической физики им.Л.Д. Ландау РАН
ведущий научный сотрудник

1992 - наст. время
Независимый Московский Университет
профессор

Временные позиции

1991 - наст. время
Математический институт Киото, Япония

Учебные курсы

• Научно-исследовательский семинар кафедры дискретной математики (уч. год: 2009–2010; Бакалавриат; где читается: Факультет математики; 2-й курс, 1-5 модуль)
• Топология (уч. год: 2009–2010; Бакалавриат; где читается: Факультет математики; 2-й курс, 1-3 модуль)

Публикации

 

Редактированные книги

Topics in quantum groups and finite-type invariants.
Mathematics at the Independent University of Moscow. Edited by B. Feigin and V. Vassiliev. American Mathematical Society Translations, Series 2, 185. Advances in the Mathematical Sciences, 38. American Mathematical Society, Providence, RI, 1998. xiv+182 pp.

Статьи

(joint with Fiegin E., Jimbo M., Miwa T., Takeyama Y.)
A $\phi\sb {1,3}$-filtration of the Virasoro minimal series $M(p,p')$ with $1<p'<p<2$.
Publ. Res. Inst. Math. Sci. 44 (2008), no. 2, 213-257.

(joint with Jimbo M., Miwa T., Mukhin E., Takeyama Y.)
Sets of rigid paths with Virasoro characters.
Ramanujan J. 15 (2008), no. 1, 123-145.

(joint with Shoikhet, Boris)
On $[A,A]/[A,[A,A]]$ and on a $W\sb n$-action on the consecutive commutators of free associative algebras.
Math. Res. Lett. 14 (2007), no. 5, 781-795.

(joint with Feigin, E.)
Two-dimensional current algebras and affine fusion product.
J. Algebra 313 (2007), no. 1, 176-198.

(joint with Gainutdinov, A. M.; Semikhatov, A. M.; Tipunin, I. Yu.)
Kazhdan-Lusztig-dual quantum group for logarithimic extensions of Virasoro minimal models.
J. Math. Phys. 48 (2007), no. 3, 032303, 46 pp.

(совм. с А.М.Гайнутдиновым, А.М.Семихатовым и И.Ю.Типуниным)
Соответствие Каждана-Люстига для категории представлений триплетной$W$-алгебры в логарифмических конформных теориях поля,
Теор. Мат. Физ., 148 (2006), no. 3, 398-427;
translation in Theoret. and Math. Phys. 148 (2006), no. 3, 1210-1235.

(joint with Gainutdinov, A. M.; Semikhatov, A. M.; Tipunin, I. Yu.)
Logarithmic extensions of minimal models: characters and modular transformations.
Nuclear Phys. B 757 (2006), no. 3, 303-343.

(joint with Feigin, E.)
Principal subspace for the bosonic vertex operator $\phi\sb {\sqrt{2m}}(z)$ and Jack polynomials.
Adv. Math. 206 (2006), no. 2, 307-328.

(joint with Gainutdinov, A. M.; Semikhatov, A. M.; Tipunin, I. Yu.)
Modular group representations and fusion in logarithmic conformal field theories and in the quantum group center.
Comm. Math. Phys. 265 (2006), no. 1, 47-93.

(joint with Feigin, Evgeny)
Homological realization of restricted Kostka polynomials.
Int. Math. Res. Not. 2005, no. 33, 1997-2029.

(joint with Jimbo, M.; Miwa, T.; Mukhin, E.; Takeyama, Y.)
A monomial basis for the Virasoro minimal series $M(p,p')$: the case $1<p'/p<2$.
Comm. Math. Phys. 257 (2005), no. 2, 395-423.

(joint with Felder, Giovanni; Shoikhet, Boris)
Hochschild cohomology of the Weyl algebra and traces in deformation quantization.
Duke Math. J. 127 (2005), no. 3, 487-517.

(joint with Jimbo, M.; Kedem, R.; Loktev, S.; Miwa, T.)
Spaces of coinvariants and fusion product. I. From equivalence theorem to Kostka polynomials.
Duke Math. J. 125 (2004), no. 3, 549-588.

(joint with Loktev, S.)
Deformation of Weyl modules and generalized parking functions.
Int. Math. Res. Not. 2004, no. 51, 2719-2750.

(joint with Loktev, S.)
Multi-dimensional Weyl modules and symmetric functions.
Comm. Math. Phys. 251 (2004), no. 3, 427-445.

(joint with Jimbo, M.; Kashiwara, M.; Miwa, T.; Mukhin, E.; Takeyama, Y.)
A functional model for the tensor product of level 1 highest and level $-1$ lowest modules for the quantum affine algebra $U\sb q(\widehat{\germ{sl}}\sb 2)$.
European J. Combin. 25 (2004), no. 8, 1197-1229.

(joint with Semikhatov, A. M.)
$\scr W\sp {(2)}\sb n$ algebras.
Nuclear Phys. B 698 (2004), no. 3, 409-449.

(joint with Jimbo, M.; Loktev, S.; Miwa, T.)
Two character formulas for $\widehat{\germ {sl}}\sb 2$ spaces of coinvariants.
Proceedings of 6th International Workshop on Conformal Field Theory and Integrable Models. Internat. J. Modern Phys. A 19 (2004), May, suppl., 134-154.

(joint with Jimbo, M.; Kedem, R.; Loktev, S.; Miwa, T.)
Spaces of coinvariants and fusion product. II. $\widehat{\germ s\germ l}\sb 2$ character formulas in terms of Kostka polynomials.
J. Algebra 279 (2004), no. 1, 147-179.

(joint with Feigin, Evgeny)
Schubert varieties and the fusion products.
Publ. Res. Inst. Math. Sci. 40 (2004), no. 3, 625-668.

(joint with Jimbo, Michio; Miwa, Tetsuji; Mukhin, Eugene; Takeyama, Yoshihiro)
Particle content of the $(k,3)$-configurations.
Publ. Res. Inst. Math. Sci. 40 (2004), no. 1, 163-220.

(joint with Jimbo, Michio; Miwa, Tetsuji; Mukhin, Eugene; Takeyama, Yoshihiro)
Fermionic formulas for $(k,3)$-admissible configurations.
Publ. Res. Inst. Math. Sci. 40 (2004), no. 1, 125-162.

(совм. с Е.Фейгиным)
Интегрируемые $sl2$- модули как бесконечные тезорные произведения
в: Фундаментальная математика сегодня, 304-334, НМУ, М., 2003.

(joint with Hong, Jin; Miwa, Tetsuji)
A construction of level 1 irreducible modules for $U\sb q(\widehat{\germ s\germ p}\sb 4)$ > using level 2 intertwiners for $U\sb q(\widehat{\germ s\germ l}\sb 2)$.
Mosc. Math. J. 3 (2003), no. 4, 1247-1267.

(joint with Jimbo, M.; Loktev, S.; Miwa, T.; Mukhin, E.)
Addendum to: "Bosonic formulas for $(k,l)$-admissible partitions"
[Ramanujan J. 7 (2003), no. 4, 485-517].
Ramanujan J. 7 (2003), no. 4, 519-530.

(joint with Jimbo, M.; Loktev, S.; Miwa, T.; Mukhin, E.)
Bosonic formulas for $(k,l)$-admissible partitions.
Ramanujan J. 7 (2003), no. 4, 485-517.

(joint with Jimbo, M.; Miwa, T.; Mukhin, E.)
Symmetric polynomials vanishing on the shifted diagonals and Macdonald polynomials.
Int. Math. Res. Not. 2003, no. 18, 1015-1034.

(joint with Jimbo, M.; Miwa, T.; Mukhin, E.; Takeyama, Y.)
Symmetric polynomials vanishing on the diagonals shifted by roots of unity.
Int. Math. Res. Not. 2003, no. 18, 999-1014.

(joint with Feigin, E.)
$Q$-characters of the tensor products in $\germ s\germ l\sb 2$-case.
Dedicated to Yuri I. Manin on the occasion of his 65th birthday. Mosc. Math. J. 2 (2002), no. 3, 567-588.

(joint with Kedem, R.; Loktev, S.; Miwa, T.; Mukhin, E.)
Combinatorics of the $\widehat{\germ{sl}}\sb 2$ coinvariants: dual functional realization and recursion.
Compositio Math. 134 (2002), no. 2, 193-241.

(joint with Kedem, R.; Loktev, S.; Miwa, T.; Mukhin, E.)
Combinatorics of the $\widehat{\germ s\germ l}\sb 2$ spaces of coinvariants: loop Heisenberg modules and recursion.
Selecta Math. (N.S.) 8 (2002), no. 3, 419-474.

(joint with Loktev, S. A.; Tipunin, I. Yu.)
Coinvariants for lattice VOAs and $q$-supernomial coefficients.
Comm. Math. Phys. 229 (2002), no. 2, 271-292.

(joint with Jimbo, Michio; Miwa, Tetsuji)
Vertex operator algebra arising from the minimal series $M(3,p)$ and monomial basis.
MathPhys odyssey, 2001, 179-204,
Prog. Math. Phys., 23, Birkhauser Boston, Boston, MA, 2002.

(joint with Jimbo, M.; Miwa, T.; Mukhin, E.)
A differential ideal of symmetric polynomials spanned by Jack polynomials at $\beta=-(r-1)/(k+1)$.
Int. Math. Res. Not. 2002, no. 23, 1223-1237.

(joint with Semikhatov, A. M.; Tipunin, I. Yu.)
Possible applications of the semi-infinite construction to integrable lattice models and the modular functor in CFT.
Quantization, gauge theory, and strings, Vol. I (Moscow, 2000), 488-494, Sci. World, Moscow, 2001.

(joint with Semikhatov, A. M.) Commutant of the $D\sb q(2\vert 1;\alpha)$ quantum group.
Quantization, gauge theory, and strings, Vol. I (Moscow, 2000), 475-487, Sci. World, Moscow, 2001.

(joint with Belavin, A. A.; Gubanov, S. Yu.)
Truncation of functional relations in the $XXZ$ model.
Mosc. Math. J. 1 (2001), no. 2, 145-156, 303.

(joint with Odesskii, A. V.)
Quantized moduli spaces of the bundles on the elliptic curve and their applications.
Integrable structures of exactly solvable two-dimensional models of quantum field theory (Kiev, 2000), 123-137,
NATO Sci. Ser. II Math. Phys. Chem., 35,
Kluwer Acad. Publ., Dordrecht, 2001.

(joint with Odesskii, A. V.)
Functional realization of some elliptic Hamiltonian structures and bosonization of the corresponding quantum algebras.
Integrable structures of exactly solvable two-dimensional models of quantum field theory (Kiev, 2000), 109-122,
NATO Sci. Ser. II Math. Phys. Chem., 35,
Kluwer Acad. Publ., Dordrecht, 2001.

(совм. с А.М.Семихатовым и И.Ю.Типуниным)
Полубесконечная реализация унитарных представлений $N=2$ алгебрыи связанные с этим конструкции.
Теор. Мат. Физ. 126 (2001), no. 1, 3-62;
translation in Theoret. and Math. Phys. 126 (2001), no. 1, 1-47.

(joint with Semikhatov, A. M.)
The $\widehat{\rm sl}(2)\oplus\widehat{\rm sl}(2)/\widehat{\rm sl}(2)$ coset theory as a Hamiltonian reduction of $\widehat D(2\vert 1;\alpha)$.
Nuclear Phys. B 610 (2001), no. 3, 489-530.

(совм. с А.Локтевым)
О финитизации тождеств Гордона,
Функ. Анал. Прил., 35 (2001), no. 1, 53-61, 96;
translation in Funct. Anal. Appl. 35 (2001), no. 1, 44-51.

(joint with Kedem, R.; Loktev, S.; Miwa, T.; Mukhin, E.)
Combinatorics of the $\widehat{\germ{sl}}\sb 2$ spaces of coinvariants.
Transform. Groups 6 (2001), no. 1, 25-52.

(joint with Ding, Jintai)
Drinfeld realization of quantum superalgebras and $U\sb q(\widehat{\germ{osp}}(1,2))$.
Conference Moshe Flato 1999, Vol. II (Dijon), 93-104,
Math. Phys. Stud., 22, Kluwer Acad. Publ., Dordrecht, 2000.

(joint with Bowcock, P.; Semikhatov, A. M.; Taormina, A.)
$\widehat{\rm sl}(2\vert 1)$ and $\widehat{D}(2\vert 1;\alpha)$ as vertex operator extensions of dual affine ${\rm sl}(2)$ algebras.
Comm. Math. Phys. 214 (2000), no. 3, 495-545.

(joint with Ding, Jintai)
Commutative quantum current operators, semi-infinite construction and functional models.
Represent. Theory 4 (2000), 330-341 (electronic).

(joint with Ding, Jintai)
Quantized $W$-algebra of $\germ s\germ l(2,1)$ and quantum parafermions of $U\sb q(\widehat{\germ s\germ l}(2))$.
J. Nonlinear Math. Phys. 7 (2000), no. 2, 170-183.

(joint with Fuks D.B.)
Cohomologies of Lie groups and Lie algebras.
Lie groups and Lie algebras, II, 125-223, Encyclopaedia Math. Sci., 21, Springer, Berlin, 2000.

(совм. с А.М.Семихатовым)
Резольвенты унитарных представлений $N=2$ алгебры Вирасоро в терминах свободных полей II. Резольвента бабочки
Теор. Мат. Физ., 121 (1999), no. 2, 244-257;
translation in Theoret. and Math. Phys. 121 (1999), no. 2, 1462-1472.

(joint with Ding, Jintai)
Quantized $W$-algebra of $\germ{sl}(2,1)$: a construction from the quantization of screening operators.
Recent developments in quantum affine algebras and related topics (Raleigh, NC, 1998), 83-108, Contemp. Math., 248,
Amer. Math. Soc., Providence, RI, 1999.

(joint with Sossinsky, Alexei; Tabachnikov, Sergei; Roger, Claude; Astashkevich, Alexander; Schwarz, Albert)
Appendix. Personal notes.
Differential topology, infinite-dimensional Lie algebras, and applications, 301-313, Amer. Math. Soc. Transl. Ser. 2, 194, Amer. Math. Soc., Providence, RI, 1999.

(joint with Finkelberg, Michael; Kuznetsov, Alexander; Mirkovic, Ivan)
Semi-infinite flags. II. Local and global intersection cohomology of quasimaps' spaces.
Differential topology, infinite-dimensional Lie algebras, and applications, 113-148, Amer. Math. Soc. Transl. Ser. 2, 194,
Amer. Math. Soc., Providence, RI, 1999.

(joint with Loktev, S.)
On generalized Kostka polynomials and the quantum Verlinde rule.
Differential topology, infinite-dimensional Lie algebras, and applications, 61-79, Amer. Math. Soc. Transl. Ser. 2, 194,
Amer. Math. Soc., Providence, RI, 1999.

(joint with Frenkel, Edward)
Integrable hierarchies and Wakimoto modules.
Differential topology, infinite-dimensional Lie algebras, and applications, 27-60, Amer. Math. Soc. Transl. Ser. 2, 194,
Amer. Math. Soc., Providence, RI, 1999.

(joint with Miwa, Tetsuji)
Extended vertex operator algebras and monomial bases.
Statistical physics on the eve of the 21st century, 366-390, Ser. Adv. Statist. Mech., 14, World Sci. Publ., River Edge, NJ, 1999.

(joint with Semikhatov, A. M.; Sirota, V. A.; Tipunin, I. Yu.)
Resolutions and characters of irreducible representations of the $N=2$ superconformal algebra.
Nuclear Phys. B 536 (1999), no. 3, 617-656.

(joint with Odesskii, A. V.)
Vector bundles on an elliptic curve and Sklyanin algebras.
Topics in quantum groups and finite-type invariants, 65-84, Amer. Math. Soc. Transl. Ser. 2, 185,
Amer. Math. Soc., Providence, RI, 1998.

(joint with Odesskii, A. V.)
Coordinate ring of the quantum Grassmannian and intertwiners for the representations of Sklyanin algebras.
Topics in quantum groups and finite-type invariants, 55-64, Amer. Math. Soc. Transl. Ser. 2, 185,
Amer. Math. Soc., Providence, RI, 1998.

(joint with Semikhatov, A. M.; Tipunin, I. Yu.)
Equivalence between chain categories of representations of affine ${\rm sl}(2)$ and $N=2$ superconformal algebras.
J. Math. Phys. 39 (1998), no. 7, 3865-3905.

(joint with Jimbo, Michio; Miwa, Tetsuji; Odesskii, Alexandr; Pugai, Yaroslav)
Algebra of screening operators for the deformed $W\sb n$ algebra.
Comm. Math. Phys. 191 (1998), no. 3, 501-541.

(joint with Enriquez, B.; Rubtsov, V.)
Separation of variables for Gaudin-Calogero systems.
Compositio Math. 110 (1998), no. 1, 1-16.

(совм. с А.В.Одесским)
Эллиптические деформации алгебр токов и их представлений разностными операторами,
Функ. Анал. Прил., 31 (1997), no. 3, 57-70, 96; t
ranslation in Funct. Anal. Appl. 31 (1997), no. 3, 193-203 (1998).

(joint with Odesskii, Alexander)
A family of elliptic algebras.
Internat. Math. Res. Notices 1997, no. 11, 531-539.

(joint with Ding, Jintai)
Quantum current operators. II. Difference equations of quantum current operators and quantum parafermion construction.
Publ. Res. Inst. Math. Sci. 33 (1997), no. 2, 285-300.

(joint with Malikov, Feodor)
Modular functor and representation theory of $\widehat{\rm sl}\sb 2$ at a rational level.
Operads: Proceedings of Renaissance Conferences (Hartford, CT/Luminy, 1995), 357-405,
Contemp. Math., 202, Amer. Math. Soc., Providence, RI, 1997.

(joint with Antonov, Alexander)
Quantum group representations and the Baxter equation.
Phys. Lett. B 392 (1997), no. 1-2, 115-122.

(совм. с С.А.Локтевым)
Когомологии нильпотентных подалгебр алгебры $sl2$,
Функ. Анал. Прил., 30 (1996), no. 4, 80-83;
translation in Funct. Anal. Appl. 30 (1996), no. 4, 285-287 (1997).

(joint with Frenkel, Edward)
Integrals of motion and quantum groups.
Integrable systems and quantum groups (Montecatini Terme, 1993), 349-418,
Lecture Notes in Math., 1620, Springer, Berlin, 1996.

(joint with Frenkel, Edward)
Quantum $\scr W$-algebras and elliptic algebras.
Comm. Math. Phys. 178 (1996), no. 3, 653-678.

(joint with Parkhomenko, S.)
Regular representation of affine Kac-Moody algebras.
Algebraic and geometric methods in mathematical physics (Kaciveli, 1993), 415-424,
Math. Phys. Stud., 19, Kluwer Acad. Publ., Dordrecht, 1996.

(совм. с Б. Энриквесом)
Интегралы движения классической системы sine-Гордон на решетке,
Теор. Мат. Физ., 103 (1995), no. 3, 507-528;
translation in Theoret. and Math. Phys. 103 (1995), no. 3, 738-756.

(joint with Enriquez, B.)
Integrals of motion of classical lattice sine-Gordon system.
R.C.P. 25, Vol. 47 (Strasbourg, 1993-1995), 127-150,
Prepubl. Inst. Rech. Math. Av., 1995/24, Univ. Louis Pasteur, Strasbourg, 1995.

(совм. с А.В.Одесским)
Эллиптические алгебры Склянина. Случай точки конечного порядка.
Функ. Анал. Прил., 29 (1995), no. 2, 9-21, 95;
translation in Funct. Anal. Appl. 29 (1995), no. 2, 81-90.

(joint with Schechtman, Vadim; Varchenko, Alexander)
On algebraic equations satisfied by hypergeometric correlators in WZW models. II.
Comm. Math. Phys. 170 (1995), no. 1, 219-247.

(joint with Frenkel, Edward)
Kac-Moody groups and integrability of soliton equations.
Invent. Math. 120 (1995), no. 2, 379-408.

(joint with Andreev, Oleg)
On bosonization of $2$d conformal field theories.
Nuclear Phys. B 433 (1995), no. 3, 685-711.

(совм. с А.В.Стояновским)
Реализация модулярного функтора в пространстве дифференциалови геометрическая аппроксимация многообразия модулей $G$-расслоений.
Функ. Анал. Прил., 28 (1994), no. 4, 42-65, 95;
translation in Funct. Anal. Appl. 28 (1994), no. 4, 257-275 (1995).

(joint with Frenkel, Edward; Reshetikhin, Nikolai)
Gaudin model, Bethe ansatz and critical level.
Comm. Math. Phys. 166 (1994), no. 1, 27-62.

(joint with Malikov, Feodor)
Fusion algebra at a rational level and cohomology of nilpotent subalgebras of $\widehat{{\germ s}{\germ l}}(2)$.
Lett. Math. Phys. 31 (1994), no. 4, 315-325.

(joint with Schechtman, Vadim; Varchenko, Alexander)
On algebraic equations satisfied by hypergeometric correlators in WZW models. I.
Comm. Math. Phys. 163 (1994), no. 1, 173-184.

(совм. с А.В.Стояновским)
Функциональные модели представлений алгебр токов и полубесконечные клетки Шуберта.
Функ. Анал. Прил., 28 (1994), no. 1, 68-90, 96;
translation in Funct. Anal. Appl. 28 (1994), no. 1, 55-72.

(joint with Malikov, Feodor)
Integral intertwining operators and complex powers of differential and $q$-difference operators.
Unconventional Lie algebras, 15-63.
Adv. Soviet Math., 17, Amer. Math. Soc., Providence, RI, 1993.

(joint with Frenkel, Edward)
Coinvariants of nilpotent subalgebras of the Virasoro algebra and partition identities.
I. M. Gelfand Seminar, 139-148, Adv. Soviet Math., 16, Part 1,
Amer. Math. Soc., Providence, RI, 1993.

(совм. с А.В.Одесским)
Конструкции эллиптических алгебр Склянина и квантовых $R$-матриц,
Функ. Анал. Прил., 27 (1993), no. 1, 37-45;
translation in Funct. Anal. Appl. 27 (1993), no. 1, 31-38.

(joint with Nakanishi, Tomoki; Ooguri, Hirosi)
The annihilating ideals of minimal models.
Infinite analysis, Part A, B (Kyoto, 1991), 217-238,
Adv. Ser. Math. Phys., 16, World Sci. Publ., River Edge, NJ, 1992.

(joint with Frenkel, Edward)
Affine Kac-Moody algebras at the critical level and Gelfand-Dikii algebras.
Infinite analysis, Part A, B (Kyoto, 1991), 197-215,
Adv. Ser. Math. Phys., 16, World Sci. Publ., River Edge, NJ, 1992.

(joint with Frenkel, Edward)
Erratum: "Semi-infinite Weil complex and the Virasoro algebra"
[Comm. Math. Phys. 137 (1991), no. 3, 617-639]. Comm. Math. Phys. 147 (1992), no. 3, 647-648.

(joint with Frenkel, Edward)
Free field resolutions in affine Toda field theories.
Phys. Lett. B 276 (1992), no. 1-2, 79-86.

Differential operators on the moduli space of $G$-bundles on algebraic curve and Lie algebra cohomologies.
Special functions (Okayama, 1990), 90-103, ICM-90 Satell. Conf. Proc., Springer, Tokyo, 1991.

Conformal field theory and cohomologies of the Lie algebra of holomorphic vector fields on a complex curve.
Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990), 71-85, Math. Soc. Japan, Tokyo, 1991.

(joint with Frenkel, Edward)
Duality in $W$-algebras.
Internat. Math. Res. Notices 1991, no. 6, 75-82.

(joint with Frenkel, Edward)
Semi-infinite Weil complex and the Virasoro algebra.
Comm. Math. Phys. 137 (1991), no. 3, 617-639.

The conformal field theory from the view of the cohomology theory of the Lie algebras.
A plenary address presented at the International Congress of Mathematicians held in Kyoto, August 1990.
ICM-90. Mathematical Society of Japan, Tokyo;
distributed outside Asia by the American Mathematical Society, Providence, RI, 1990.

(joint with Fuchs, D. B.)
Representations of the Virasoro algebra.
Representation of Lie groups and related topics, 465-554,
Adv. Stud. Contemp. Math., 7, Gordon and Breach, New York, 1990.

(joint with Frenkel, Edward V.)
Representations of affine Kac-Moody algebras and bosonization.
Physics and mathematics of strings, 271-316, World Sci. Publ., Teaneck, NJ, 1990.

(joint with Schechtman, V. V.; Varchenko, A. N.)
On algebraic equations satisfied by correlators in Wess-Zumino-Witten models.
Lett. Math. Phys. 20 (1990), no. 4, 291-297.

(joint with Frenkel, Edward)
Quantization of the Drinfeld-Sokolov reduction.
Phys. Lett. B 246 (1990), no. 1-2, 75-81.

(joint with Frenkel, Edward)
Bosonic ghost system and the Virasoro algebra.
Phys. Lett. B 246 (1990), no. 1-2, 71-74.

(joint with Frenkel, Edward V.)
Representations of affine Kac-Moody algebras, bosonization and resolutions.
Lett. Math. Phys. 19 (1990), no. 4, 307-317.

(joint with Frenkel, Edward V.)
Affine Kac-Moody algebras and semi-infinite flag manifolds.
Comm. Math. Phys. 128 (1990), no. 1, 161-189.

(совм. с А.В.Одесским)
Эллиптические алгебры Склянина
Функ. Анал. Прил., 23 (1989), no. 3, 45-54, 96;
translation in Funct. Anal. Appl. 23 (1989), no. 3, 207-214 (1990).

(joint with Tsygan, B. L.)
Riemann-Roch theorem and Lie algebra cohomology. I.
Proceedings of the Winter School on Geometry and Physics (Srn?, 1988).
Rend. Circ. Mat. Palermo (2) Suppl. No. 21 (1989), 15-52.

(joint with Schechtman, V.)
The honour to V. Knizhnik.
Proceedings of the Winter School on Geometry and Physics (Srn?, 1988).
Rend. Circ. Mat. Palermo (2) Suppl. No. 21 (1989), 9-10.

(joint with Fialowski, A.)
Cohomology of the nilpotent subalgebras of current Lie algebras.
Studia Sci. Math. Hungar. 24 (1989), no. 1, 1-9.

(joint with Fuchs, D. B.)
Cohomology of some nilpotent subalgebras of the Virasoro and Kac-Moody Lie algebras.
J. Geom. Phys. 5 (1988), no. 2, 209-235.

(совм. с Э.В.Френкелем)
Семейство представлений аффинных алгебр Ли,
УМН, 43 (1988), no. 5(263), 227-228;
translation in Russian Math. Surveys 43 (1988), no. 5, 221-222.

(joint with Fuchs, D. B.; Retakh, V. S.)
Massey operations in the cohomology of the infinite-dimensional Lie algebra $L\sb 1$.
Topology and geometry—-Rohlin Seminar, 13-31,
Lecture Notes in Math., 1346, Springer, Berlin, 1988.

(совм. с Д.Б.Фуксом)
Когомологии групп Ли и алгебр Ли,
в: Современные проблемы математики. Фундаментальные направления, т. 21, 121-209, 215, Итоги науки и техники, АН СССР, ВИНИТИ, М., 1988.

On the cohomology of the Lie algebra of vector fields and of the current algebra.
Selected translations. Selecta Math. Soviet. 7 (1988), no. 1, 49-62.

Алгебры Ли ${\rm gl}(\lambda)$ и когомологии алгебры Ли дифференциальных операторов.
УМН, 43 (1988), no. 2(260), 157-158;
translation in Russian Math. Surveys 43 (1988), no. 2, 169-170.

(joint with Tsygan, B. L.)
Cyclic homology of algebras with quadratic relations, universal enveloping algebras and group algebras.
$K$-theory, arithmetic and geometry (Moscow, 1984-1986), 210-239,
Lecture Notes in Math., 1289, Springer, Berlin, 1987.

(joint with Tsygan, B. L.)
Additive $K$-theory.
$K$-theory, arithmetic and geometry (Moscow, 1984-1986), 67-209,
Lecture Notes in Math., 1289, Springer, Berlin, 1987.

(joint with Fialowski, A.)
Cohomology of the infinite-dimensional Lie algebra $L\sb 1$ with nontrivial coefficients.
Bull. Amer. Math. Soc. (N.S.) 17 (1987), no. 2, 333-337.

(совм. с Ф.Г.Маликовым и Д.Б.Фуксом)
Особые векторы в модулях Верма над алгебрами Каца-Муди,
Функ. Анал. Прил., 20 (1986), no. 2, 25-37, 96.

(joint with Leites, D. A.; Serganova, V. V.)
Kac-Moody superalgebras.
Group theoretical methods in physics, Vol. 1-3 (Zvenigorod, 1982), 631-637,
Harwood Academic Publ., Chur, 1985.

(joint with Leites, D. A.)
New Lie superalgebras of string theories.
Group theoretical methods in physics, Vol. 1-3 (Zvenigorod, 1982), 623-629,
Harwood Academic Publ., Chur, 1985.

(joint with Zelevinsky, A. V.)
Representations of contragredient Lie algebras and the Kac-Macdonald identities.
Representations of Lie groups and Lie algebras (Budapest, 1971), 25-77,
Akad. Kiad?, Budapest, 1985.

(совм. с Б.Л.Цыганом)
Аддитивная $K$-теория и кристалинные когомологии,
Функ. Анал. Прил., 19 (1985), no. 2, 52-62, 96.

(joint with Fuchs, D. B.)
Verma modules over the Virasoro algebra.
Topology (Leningrad, 1982), 230-245,
Lecture Notes in Math., 1060, Springer, Berlin, 1984.

(совм. с Д.Б.Фуксом)
Стабильные когомологии алгебры $W\sb{n}$ и соотношения в алгебре $L\sb{1}$,
Функ. Анал. Прил., 18 (1984), no. 3, 94-95.

Полубесконечные гомологии алгебр Ли. Каца-Муди и Вирасоро,
УМН, 39 (1984), no. 2(236), 195-196.

(совм. с А.Фиаловски)
Когомологии нильпотентов алгебр токов,
ДАН СССР, 271 (1983), no. 4, 813-816.

(совм. с Д.Б.Фуксом)
Модули Верма над алгеброй Вирасоро,
Функ. Анал. Прил., 17 (1983), no. 3, 91-92.

(совм. с Д.Б.Фуксом)
Операторы Казимира в модулях над алгеброй Вирасоро,
ДАН СССР, 269 (1983), no. 5, 1057-1060.

(совм. с Б.Л.Цыганом)
Когомологии алгебр Ли обобщенных матриц Якоби,
Функ. Анал. Прил., 17 (1983), no. 2, 86-87.

(совм. с В.С.Ретахом)
Когомологии некоторых алгебр Ли и супералгебр векторных полей,
УМН, 37 (1982), no. 2(224), 233-234.

Когомологии контактных алгебр Ли,
Cohomology of contact Lie algebras.
(Russian) C. R. Acad. Bulgare Sci. 35 (1982), no. 8, 1029-1031.

(совм. с Д.Б.Фуксом)
Кососимметрические инварианты дифференциальных операторов на прямойи модули Верма над алгеброй Вирасоро,
Функ. Анал. Прил., 16 (1982), no. 2, 47-63, 96.

(совм. с Д.Б.Фуксом)
Гомологии алгебры Ли векторных полей на прямой,
Функ. Анал. Прил., 14 (1980), no. 3, 45-60, 96.

Когомологии групп и алгебр токов,
УМН, 35 (1980), no. 2(212), 225-226.

(совм. с Д.Б.Фуксом)
Инвариантные дифференциальные операторы на прямой,
Функ. Анал. Прил., 13 (1979), no. 4, 91-92.

(совм. с И.М.Гельфандом и Д.Б.Фуксом)
Когомологии бесконечномерных алгебр Ли и операторы Лапласа,
Функ. Анал. Прил., 12 (1978), no. 4, 1-5.

Характеристические классы флагов слоений,
Функ. Анал. Прил., 9 (1975), no. 4, 49-56.

(совм. с И.М.Гельфандом и Д.Б.Фуксом)
Когомологии алгебры Ли формальных векторных полей с коэффициентамив двойственном пространстве и вариации характеристиеческих классов слоений,
Функ. Анал. Прил., 8 (1974), no. 2, 13-29.