167 citations · 1.9k across the 134 of their papers we have counts for
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Hypergeometric integrals, hook formulas and Whittaker vectors
G. Felder, A. Smirnov, V. Tarasov +1
We determine the coefficient of proportionality between two multidimensional hypergeometric integrals. One of them is a solution of the dynamical difference equations associated wi…
Polynomial superpotential for Grassmannian from a limit of vertex function
Andrey Smirnov, Alexander Varchenko
In this note we discuss an integral representation for the vertex function of the cotangent bundle over the Grassmannian, . This integral representation can be use…
The p-adic approximations of vertex functions via 3D-mirror symmetry
Andrey Smirnov, Alexander Varchenko
Using the mirror symmetry we construct a system of polynomials with integral coefficients which solve the quantum differential equitation of modulo…
Monodromy of the equivariant quantum differential equation of the cotangent bundle of a Grassmannian
Vitaly Tarasov, Alexander Varchenko
We describe the monodromy of the equivariant quantum differential equation of the cotangent bundle of a Grassmannian in terms of the equivariant K-theory algebra of the cotangent b…
Landau-Ginzburg mirror, quantum differential equations and qKZ difference equations for a partial flag variety
Vitaly Tarasov, Alexander Varchenko
We consider the system of quantum differential equations for a partial flag variety and construct a basis of solutions in the form of multidimensional hypergeometric functions, tha…
On the number of -hypergeometric solutions of KZ equations
Alexander Varchenko
It is known that solutions of the KZ equations can be written in the form of multidimensional hypergeometric integrals. In 2017 in a joint paper of the author with V. Schechtman th…
Dynamical Bethe algebra and functions on pairs of quasi-polynomials
A. Slinkin, D. Thompson, A. Varchenko
We consider the space of functions on the Cartan subalgebra of with values in the zero weight subspace of a tensor product of ir…
Incarnations of XXX Bethe ansatz equations and integrable hierarchies
Igor Krichever, Alexander Varchenko
We consider the space of solutions of the Bethe ansatz equations of the XXX quantum integrable model, associated with the trivial representation of $\wideha…
Dynamical elliptic Bethe algebra, KZB eigenfunctions, and theta-polynomials
Daniel Thompson, Alexander Varchenko
Let be the zero weight subspace of a tensor product of finite-dimensional irreducible -modules. The dynamical elliptic Bethe algebra is a com…
Extended Joseph polynomials, quantized conformal blocks, and a q-Selberg type integral
R. Rimányi, V. Tarasov, A. Varchenko +1
We consider the tensor power of the vector representation of and its weight decomposition . For $λ= (λ_1 \geq ... \geq…
Conformal blocks and equivariant cohomology
R. Rimányi, V. Schechtman, A. Varchenko
We show that the conformal blocks constructed in the previous article by the first and the third author may be described as certain integrals in equivariant cohomology. When the bu…