167 citations · 1.9k across the 134 of their papers we have counts for
9 papers · 1 filter
Potentials of a Frobenius like structure
Claus Hertling, Alexander Varchenko
This paper proves the existence of potentials of the first and second kind of a Frobenius like structure in a frame which encompasses families of arrangements. The frame uses the n…
Solutions modulo of Gauss-Manin differential equations for multidimensional hypergeometric integrals and associated Bethe ansatz
Alexander Varchenko
We consider the Gauss-Manin differential equations for hypergeometric integrals associated with a family of weighted arrangements of hyperplanes moving parallelly to themselves. We…
-Hypergeometric solutions of quantum differential equations, quantum Pieri rules, and Gamma theorem
Vitaly Tarasov, Alexander Varchenko
We describe \,-hypergeometric solutions of the equivariant quantum differential equations and associated qKZ difference equations for the cotangent bundle of a partial…
Remarks on the Gaudin model modulo
Alexander Varchenko
We discuss the Bethe ansatz in the Gaudin model on the tensor product of finite-dimensional -modules over the field with elements, where is a prime number. We d…
Solutions of KZ differential equations modulo
Vadim Schechtman, Alexander Varchenko
We construct polynomial solutions of the KZ differential equations over a finite field as analogs of hypergeometric solutions.
Elliptic and K-theoretic stable envelopes and Newton polytopes
R. Rimányi, V. Tarasov, A. Varchenko
In this paper we consider the cotangent bundles of partial flag varieties. We construct the -theoretic stable envelopes for them and also define a version of the elliptic stable…
Self-dual Grassmannian, Wronski map, and representations of , ,
Kang Lu, E. Mukhin, A. Varchenko
We define a -stratification of the Grassmannian of planes . The -stratification consists of strata labeled by…
Critical points of master functions and mKdV hierarchy of type
Alexander Varchenko, Tyler Woodruff
We consider the population of critical points generated from the critical point of the master function with no variables, which is associated with the trivial representation of the…
Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology
Giovanni Felder, Richárd Rimányi, Alexander Varchenko
We define an elliptic version of the stable envelope of Maulik and Okounkov for the equivariant elliptic cohomology of cotangent bundles of Grassmannians. It is a version of the co…