91 citations · 871 across the 69 of their papers we have counts for
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Duality for Bethe algebras acting on polynomials in anticommuting variables
V. Tarasov, F. Uvarov
We consider actions of the current Lie algebras and on the space of polynomials in anticommuting variables. The actions depend on…
Lower bounds for numbers of real solutions in problems of Schubert calculus
E. Mukhin, V. Tarasov
We give lower bounds for the numbers of real solutions in problems appearing in Schubert calculus in the Grassmannian Gr(n,d) related to osculating flags. It is known that such sol…
On Conjectures of A. Eremenko and A. Gabrielov
E. Mukhin, V. Tarasov
We study polynomials p(x) satisfying a differential equation of the form p"(x)-h'(x)p'(x)+H(x)p(x)=0, where h(x)=x^3/3+ax. We prove a conjecture of A. Eremenko and A. Gabrielov.
Reality property of discrete Wronski map with imaginary step
E. Mukhin, V. Tarasov, A. Varchenko
For a set of quasi-exponentials with real exponents, we consider the discrete Wronskian (also known as Casorati determinant) with pure imaginary step 2h. We prove that if the coeff…
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…
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…