MS Seminar (Mathematics - String Theory)

Speaker: Ryo Fujita (Kyoto University)
Title: Coherent IC-sheaves on type $A_n$ affine Grassmannians and dual canonical basis of affine type $A_1$
Date: Thu, Apr 11, 2019, 15:30 - 17:00
Place: Seminar Room A
Abstract: The convolution ring of the equivariant K-theory of the $GL_n$ affine Grassmannian is a simplest example of the quantized K-theoretic Coulomb branch of a quiver gauge theory (for $A_1$-quiver). It was identified with a quantum unipotent cell of the loop group $LSL_2$ as a quantum cluster algebra by Cautis-Williams via their monoidal categorification theorem. In this talk, we further identify the basis formed by the classes of irreducible equivariant perverse coherent sheaves (coherent IC-sheaves) with the dual canonical basis of the quantum unipotent cell. For a proof, we apply Bezrukavnikov's theory of equivariant perverse coherent sheaves on the nilpotent cones of type A. This is a joint work with Michael Finkelberg.
Remarks: Blackboard talk