6 papers
The quantum Hikita conjecture via quasimaps
Hunter Dinkins, Ivan Karpov, Vasily Krylov
We propose a refinement of the quantum Hikita conjecture of Kamnitzer, McBreen, and Proudfoot that bridges the representation theory of Coulomb branches with the enumerative geomet…
A Hesselink-type formula for the nilpotent cone of Lie algebra representations
Vasily Krylov, Frank Wang
A well-known result of Hesselink gives a formula for the -character of the nilpotent cone of a semisimple Lie algebra in terms of a -analog of the Kostant partition function.…
Noncommutative resolutions of affine Schubert varieties in type A and canonical bases
Ilya Dumanski, Vasily Krylov
Given a resolution of an affine Schubert variety for , we define its noncommutative version -- a…
K-theory of Gieseker variety and type A cyclotomic Hecke algebra
Vasily Krylov, Raphaël Paegelow, Pavel Shlykov
We give an algebraic description of the equivariant K-theory of Gieseker varieties. Our main result identifies the equivariant K-theory of the Gieseker space with the Jucys--Murphy…
Slant sums of quiver gauge theories
Hunter Dinkins, Vasily Krylov, Reese Lance
We define the slant sum of quiver gauge theories, a gluing on the underlying quivers that identifies a gauge vertex with a framing vertex. Under some mild assumptions, we relate to…
K-theoretic Hikita conjecture for quiver gauge theories
Ilya Dumanski, Vasily Krylov
We study variants of Hikita conjecture for Nakajima quiver varieties and corresponding Coulomb branches. First, we derive the equivariant version of the conjecture from the non-equ…