Semi-infinite parabolic IC-sheaf

TL;DR

This paper constructs and studies a parabolic semi-infinite IC-sheaf on the affine Grassmannian of a reductive group, relating it to sheaves on the Drinfeld compactification and dual baby Verma objects, advancing geometric representation theory.

Contribution

It introduces the parabolic semi-infinite IC-sheaf, explores its properties, and connects it to sheaves on the Drinfeld compactification and spectral dual objects.

Findings

Construction of the parabolic semi-infinite IC-sheaf.

Establishment of its key properties.

Relation to sheaves on the Drinfeld compactification and dual baby Verma objects.

Abstract

Let G be a connected reductive group, P its parabolic subgroup. We consider the parabolic semi-infinite category of sheaves on the affine Grassmanian of G and construct the parabolic version of the semi-infinite IC-sheaf of each orbit. We establish some of its properties and relate it to sheaves on the Drinfeld compactification of the moduli stack Bun_P of P-torsors on a curve. We also relate the parabolic semi-infinite IC-sheaf with the dual baby Verma object on the spectral side.