Vasily Krylov

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math.RT2026

A formula for the $q$ -character of functions on the nilpotent cone of some Lie algebra representations

Vasily Krylov, Frank Wang

Let $g$ be a reductive Lie algebra and $V$ a finite-dimensional $g$ -representation. When $V$ is the representation of a cyclic quiver with equal dimensions, t…

math.RT2026

Noncommutative resolutions of affine Schubert varieties in type A and canonical bases

Ilya Dumanski, Vasily Krylov

Given a resolution $Gr^{I^»} \to Gr^{I^} »$ of an affine Schubert variety for $G L_{n}$ , we define its noncommutative version --…

math.RT2026

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…

math.RT2026

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…

A formula for the q-character of functions on the nilpotent cone of some Lie algebra representations

Noncommutative resolutions of affine Schubert varieties in type A and canonical bases

Slant sums of quiver gauge theories

K-theoretic Hikita conjecture for quiver gauge theories

A formula for the $q$ -character of functions on the nilpotent cone of some Lie algebra representations