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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…
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…