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math.QA2009★ 5 cited
Bethe algebra of the gl_{N+1} Gaudin model and algebra of functions on the critical set of the master function
E. Mukhin, V. Tarasov, A. Varchenko
Consider a tensor product of finite-dimensional irreducible gl_{N+1}-modules and its decomposition into irreducible modules. The gl_{N+1} Gaudin model assigns to each multiplicity…
math.QA2009★ 6 cited
Three sides of the geometric Langlands correspondence for gl_N Gaudin model and Bethe vector averaging maps
E. Mukhin, V. Tarasov, A. Varchenko
We consider the gl_N Gaudin model of a tensor power of the standard vector representation. The geometric Langlands correspondence in the Gaudin model relates the Bethe algebra of t…
math.QA2008
The gl_2 Bethe algebra associated with a nilpotent element
E. Mukhin, V. Tarasov, A. Varchenko
To any 2x2-matrix K one assigns a commutative subalgebra B^{K}\subset U(gl_2[t]) called a Bethe algebra. We describe relations between the Bethe algebras, associated with the zero…