Gaudin Model and Bender-Knuth Involutions

Student: Levin Ilya

Supervisor: Leonid Grigoryevich Rybnikov

Educational Programme: Mathematics (Master)

Year of Graduation: 2020

Fix Lie algebra gl_N. Bethe subalgebras A(z) are some maximal commutative subalgebras of n-th tensor power of universal enveloping algebra, parametrized by M_{n+1} —— the moduli space of stable curves with labeled points. It is known that for any sequence of irreducible representations, the multiplicity spaces in their tensor product can be uniquely decomposed in the sum of eigenlines for A(z), called Bethe eigenlines. We consider the case of sequence of symmetric powers of the standard representation. Modulo some technical fact, wich we haven't yet proved, we decribe monodromy of Bethe eigenlines in terms of Bender-Knuth involutions on the set of semistandard tables.

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