167 citations · 1.9k across the 134 of their papers we have counts for
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The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz
E. Mukhin, V. Tarasov, A. Varchenko
We prove the B. and M. Shapiro conjecture that says that if the Wronskian of a set of polynomials has real roots only, then the complex span of this set of polynomials has a basis…
Bispectral and $(\glN,\glM)$ Dualities
E. Mukhin, V. Tarasov, A. Varchenko
Let $V = < p_{ij}(x)e^{\la_ix}, i=1,...,n, j=1, ..., N_i >$ be a space of quasi-polynomials of dimension . Define the regularized fundamental operator of as the…
Quiver -Modules and Homology of Local Systems over an Arrangement of Hyperplanes
S. Khoroshkin, A. Varchenko
Let be an arrangement of affine hyperplanes in a complex affine space , the ring of algebraic differential operators on . We define a category of quivers associated w…
Multiplicity of critical points of master functions and Schubert calculus
Prakash Belkale, Evgeny Mukhin, Alexander Varchenko
In [MV], some correspondences were defined between critical points of master functions associated to sl_{N+1} and subspaces of C[x] with given ramification properties. In this pape…
Poincare-Birkhoff-Witt expansions of the canonical elliptic differential form
G. Felder, R. Rimanyi, A. Varchenko
We study the canonical U(\n)-valued elliptic differential form, whose projections to different Kac-Moody algebras are key ingredients of the hypergeometric integral solutions of el…
Multiple orthogonal polynomials and a counterexample to Gaudin Bethe Ansatz Conjecture
E. Mukhin, A. Varchenko
Jacobi polynomials are polynomials whose zeros form the unique solution of the Bethe Ansatz equation associated with two sl_2 irreducible modules. We study sequences of r polynomia…