Leonid Grigoryevich Rybnikov

Publications³⁴

• Article Aleksei Ilin, Mashanova-Golikova I., Leonid Rybnikov. Spectra of Bethe subalgebras of Y(gl_n) in tame representations // Letters in Mathematical Physics. 2022. Vol. 112. No. 5. Article 99. doi
• Article Aleksei Ilin, Leonid Rybnikov. On classical limits of Bethe subalgebras in Yangians // Transformation Groups. 2021. Vol. 26. No. 2. P. 537-564. doi
• Article Rybnikov L. G. A Proof of the Gaudin Bethe Ansatz Conjecture // International Mathematics Research Notices. 2020. Vol. 2020. No. 22. P. 8766-8785. doi
• Article Halacheva I., Kamnitzer J., Rybnikov L. G., Weekes A. Crystals and monodromy of Bethe vectors // Duke Mathematical Journal. 2020. Vol. 169. No. 12. P. 2337-2419. doi
• Article Aleksei Ilin, Leonid Rybnikov. Bethe Subalgebras in Yangians and the Wonderful Compactification // Communications in Mathematical Physics. 2019. Vol. 372. No. 1. P. 343-366. doi
• Article Leonid Rybnikov, Mikhail Zavalin. Gelfand–Tsetlin Degeneration of Shift of Argument Subalgebras in Types B, C and D // Arnold Mathematical Journal. 2019. Vol. 5. No. 2-3. P. 285-313. doi
• Article Leonid Rybnikov. Cactus Group and Monodromy of Bethe Vectors // International Mathematics Research Notices. 2018. No. 1. P. 202-235. doi
• Article Michael Finkelberg, Kamnitzer J., Pham K., Leonid Rybnikov, Weekes A. Comultiplication for shifted Yangians and quantum open Toda lattice // Advances in Mathematics. 2018. Vol. 327. P. 349-389. doi
• Article Aleksei Ilin, Rybnikov L. G. Degeneration of Bethe subalgebras in the Yangian of $gl_n$ // Letters in Mathematical Physics. 2018. Vol. 108. No. 4. P. 1083-1107. doi
• Article Michael Finkelberg, Alexander Kuznetsov, Leonid Rybnikov, Dobrovolska G. Towards a cluster structure on trigonometric zastava // Selecta Mathematica, New Series. 2018. Vol. 24. No. 1. P. 187-225. doi
• Preprint Aleksei Ilin, Leonid Rybnikov. Degeneration of Bethe subalgebras in the Yangian of $gl_n$ / Cornell University. Series arXiv:1703.04147 "Series math "arxiv.org"". 2017.
• Article Glutsyuk A., Rybnikov L. G. On families of differential equations on two-torus with all phase-lock areas // Nonlinearity. 2017. Vol. 30. No. 1. P. 61-72. doi
• Preprint Rybnikov L. G. A proof of the Gaudin Bethe Ansatz conjecture. / Cornell University. Series QA "arxiv.org". 2016.
• Preprint Rybnikov L. G. Cactus group and monodromy of Bethe vectors / Cornell University. Series QA "arXiv math". 2016. No. 1409.0131.
• Preprint Rybnikov L. G., Finkelberg M. V., Kamnitzer J., Weekes A., Pham K. Comultiplication for shifted Yangians and quantum open Toda lattice / Cornell University. Series arXiv:1608.03331 "Series math "arxiv.org"". 2016.
• Article Michael Finkelberg, Leonid Rybnikov, Alexander Kuznetsov, Dobrovolska G. Towards a cluster structure on trigonometric zastava // Selecta Mathematica, New Series. 2016. P. 1-39. doi (in press)
• Article Loktev S., Rybnikov L. G., Etingof P. Boris Feigin // Moscow Mathematical Journal. 2015. Vol. 15. No. 2. P. 185-186.
• Preprint Glutsyuk A., Rybnikov L. G. On families of differential equations on two-torus with all Arnold tongues / Cornell University. Series math "arxiv.org". 2015. No. 15.
• Preprint Finkelberg M. V., Kuznetsov A., Rybnikov L. G., Dobrovolska G. Towards a cluster structure on trigonometric zastava / Cornell University. Series math "arxiv.org". 2015.
• Article Finkelberg M. V., Rybnikov L. G. Quantization of Drinfeld Zastava in type A // Journal of the European Mathematical Society. 2014. Vol. 16. No. 2. P. 235-271.
• Article Finkelberg M. V., Rybnikov L. G. Quantization of Drinfeld Zastava in type С // Algebraic Geometry. 2014. Vol. 1. No. 2. P. 166-180.
• Preprint Michael Finkelberg, Leonid Rybnikov. Quantization of Drinfeld Zastava in type C / Cornell University. Series math "arxiv.org". 2013.
• Article Finkelberg M. V., Rybnikov L. G. Quantization of Drinfeld Zastavain type A // Journal of the European Mathematical Society. 2012 (in press)
• Article Braverman A., Rybnikov L. G., Feigin B. L., Finkelberg M. V. A finite analog of the AGT relation I: finite W-algebras and quasimaps' spaces // Communications in Mathematical Physics. 2011. Vol. 308. No. 2. P. 457-478. doi
• Article Feigin B. L., Finkelberg M. V., Rybnikov L. G., Frenkel I. Gelfand-Tsetlin algebras and cohomology rings of Laumon spaces // Selecta Mathematica, New Series. 2011. Vol. 17. No. 2. P. 337-361. doi
• Article Feigin B. L., Finkelberg M. V., Rybnikov L. G., Negut A. Yangians and cohomology rings of Laumon spaces // Selecta Mathematica, New Series. 2011. Vol. 17. No. 3. P. 573-607. doi
• Article Rybnikov L. G., Chervov A., Falqui G. Limits of Gaudin algebras, quantization of bending flows, Jucys-Murphy elements and Gelfand-Tsetlin bases // Letters in Mathematical Physics. 2010. Vol. 91. No. 1. P. 129-150.
• Article Feigin B. L., Rybnikov L. G., Frenkel E. Opers with irregular singularity and spectra of the shift of argument subalgebra // Duke Mathematical Journal. 2010. Vol. 155. No. 2. P. 337-363.
• Article Rybnikov L. G., Chervov A., Falqui G. Limits of Gaudin systems: classical and quantum cases // Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2009. Vol. 5. No. 29. P. 17.
• Article Frenkel E., Feigin B. L., Rybnikov L. G. On the endomorphisms of Weyl modules over affine Kac-Moody algebras at the critical level // Letters in Mathematical Physics. 2009. Vol. 88. No. 1-3. P. 163-173.
• Article Loktev S., Rybnikov L. G., Oblomkov A., Etingof P. A Lie-theoretic construction of spherical symplectic reflection algebras // Transformation Groups. 2008. Vol. 13. No. 3. P. 541-556.
• Article Rybnikov L. G. Uniqueness of higher Gaudin hamiltonians // Reports on Mathematical Physics. 2008. Vol. 61. No. 2. P. 247-252.
• Article Рыбников Л. Г. Метод сдвига инвариантов и модель Годена // Функциональный анализ и его приложения. 2006. Т. 40. № 3. С. 30-43.
• Article Рыбников Л. Г. Централизаторы некоторых квадратичных элементов в алгебрах Пуассона--Ли и метод сдвига инвариантов // Успехи математических наук. 2005. Т. 60. № 2(362). С. 173-174.