19 citations · 50 across the 7 of their papers we have counts for
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Sets of rigged paths with Virasoro characters
B. Feigin, M. Jimbo, T. Miwa +2
Let \{M_{r,s}\}_{0< r < p, 0< s < p'} be the irreducible Virasoro modules in the -minimal series. In our previous paper, we have constructed a monomial basis of \oplus_{r=1…
Norm of a Bethe Vector and the Hessian of the Master Function
Evgeny Mukhin, Alexander Varchenko
We show that the Bethe vectors are non-zero vectors in the sl_{r+1} Gaudin model. Moreover, we show that the norm of a Bethe vector is equal to the Hessian of the corresponding mas…
Miura Opers and Critical Points of Master Functions
Evgeny Mukhin, Alexander Varchenko
Critical points of a master function associated to a simple Lie algebra \g come in families called the populations [MV1]. We prove that a population is isomorphic to the flag varie…
Self-self-dual spaces of polynomials
Lev Borisov, Evgeny Mukhin
A space of polynomials V of dimension 7 is called self-dual if the divided Wronskian of any 6-subspace is in V. A self-dual space V has a natural inner product. The divided Wronski…
Populations of solutions of the XXX Bethe equations associated to Kac-Moody algebras
E. Mukhin, A. Varchenko
We consider the XXX Bethe equation associated with integral dominant weights of a Kac-Moody algebra and introduce a generating procedure constructing new solutions starting from a…
Symmetric polynomials vanishing on the diagonals shifted by roots of unity
B. Feigin, M. Jimbo, T. Miwa +2
For a pair of positive integers (k,r) with r>1 such that k+1 and r-1 are relatively prime, we describe the space of symmetric polynomials in variables x_1,...,x_n which vanish at a…