Coherent IC-sheaves on type 𝐴_{𝑛} affine Grassmannians and dual canonical basis of affine type 𝐴₁

Abstract

The convolution ring K GL n (O) C × (Gr GL n ) was identified with a quantum unipotent cell of the loop group LSL 2 in Cautis and Williams [J. Amer. Math. Soc. 32 (2019), pp. 709-778]. We identify the basis formed by the classes of irreducible equivariant perverse coherent sheaves with the dual canonical basis of the quantum unipotent cell.