167 citations · 1.9k across the 134 of their papers we have counts for
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Multiplication Formulas for the Elliptic Gamma Function
G. Felder, A. Varchenko
The elliptic gamma function is a generalization of the Euler gamma function. Its trigonometric and rational degenerations are the Jackson q-gamma function and the Euler gamma funct…
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…
Solutions to the XXX type Bethe ansatz equations and flag varieties
E. Mukhin, A. Varchenko
We consider a version of the A_N Bethe equation of XXX type and introduce a reproduction procedure constructing new solutions of this equation from a given one. The set of all solu…
Resonant local systems on complements of discriminantal arrangements and sl_2 representations
Daniel C. Cohen, Alexander N. Varchenko
We calculate the skew-symmetric cohomology of the complement of a discriminantal hyperplane arrangement with coefficients in local systems arising in the context of the representat…
Critical points of master functions and flag varieties
E. Mukhin, A. Varchenko
We consider critical points of master functions associated with integral dominant weights of Kac-Moody algebras and introduce a generating procedure constructing new critical point…
How to regularize singular vectors and kill the dynamical Weyl group
K. Styrkas, V. Tarasov, A. Varchenko
We study the meromorphic family of intertwining operators between Verma modules and their products with finite-dimensional ones. A regularizing operator, acting in a finite dimensi…
Special functions, KZ type equations and Representation theory
Alexander Varchenko
This paper is a set of lecture notes of my course "Special functions, KZ type equations, and representation theory" given at MIT during the spring semester of 2002. The notes do no…
Even powers of divisors and elliptic zeta values
Giovanni Felder, Alexander Varchenko
We introduce and study "elliptic zeta values", a two-parameter deformation of the values of Riemann's zeta function at positive integers. They are essentially Taylor coefficients o…
Modular transformations of the elliptic hypergeometric functions, Macdonald polynomials, and the shift operator
G. Felder, L. Stevens, A. Varchenko
We consider the space of elliptic hypergeometric functions of the sl_2 type associated with elliptic curves with one marked point. This space represents conformal blocks in the sl_…