11 citations · 17 across the 7 of their papers we have counts for
7 papers
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…
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…
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 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…
On reduced arc spaces of toric varieties
Ilya Dumanski, Evgeny Feigin, Ievgen Makedonskyi +1
An arc space of an affine cone over a projective toric variety is known to be non-reduced in general. It was demonstrated recently that the reduced scheme structure is worth studyi…
Beilinson-Drinfeld Schubert varieties and global Demazure modules
Ilya Dumanski, Evgeny Feigin, Michael Finkelberg
We compute the spaces of sections of powers of the determinant line bundle on the spherical Schubert subvarieties of the Beilinson- Drinfeld affine Grassmannians. The answer is giv…
Reduced arc schemes for Veronese embeddings and global Demazure modules
Ilya Dumanski, Evgeny Feigin
We consider arc spaces for the compositions of Pluecker and Veronese embeddings of the flag varieties for simple Lie groups of types ADE. The arc spaces are not reduced and we cons…