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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 of an affine Schubert variety for , we define its noncommutative version -- a…
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…
math.RT2025
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.RT2023
A geometric approach to Feigin-Loktev fusion product and cluster relations in coherent Satake category
Ilya Dumanski
We propose a geometric realization of the Feigin-Loktev fusion product of graded cyclic modules over the current algebra. This allows us to compute it in several new cases. We also…