167 citations · 1.9k across the 134 of their papers we have counts for
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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…
Solutions of the qKZ equations modulo an integer
Evgeny Mukhin, Alexander Varchenko
We study the qKZ difference equations with values in the -th tensor power of the vector representation , variables and integer step . For any intege…
Dynamical and qKZ equations modulo , an example
Alexander Varchenko
We consider an example of the joint system of dynamical differential equations and qKZ difference equations with parameters corresponding to equations for elliptic integrals. We so…
Dwork-type congruences and -adic KZ connection
Alexander Varchenko
We show that the -adic KZ connection associated with the family of curves has an invariant subbundle of rank , while the corresponding complex…
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…
Frobenius-like structure in Gaudin model
Evgeny Mukhin, Alexander Varchenko
We introduce a Frobenius-like structure for the Gaudin model. Namely, we introduce potential functions of the first and second kind. We describe the Shapovalov form i…