Ilya Dumanski

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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

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…

math.RT2025

Perverse coherent sheaves on symplectic singularities

Ilya Dumanski

We propose the notion of perverse coherent sheaves for symplectic singularities and study its properties. In particular, it gives a basis of simple objects in the Grothendieck grou…