Perverse sheaves on a Loop group and Langlands' duality

TL;DR

This paper constructs a tensor category of perverse sheaves on the loop group LG to study the affine Grassmannian's topology and establish a Langlands duality correspondence for automorphic sheaves.

Contribution

It provides an intrinsic construction of the tensor category of representations of the Langlands dual group using perverse sheaves on LG, linking geometric and representation-theoretic aspects.

Findings

Tensor category of representations constructed via perverse sheaves.

Application to topology of the affine Grassmannian.

Establishment of a Langlands-type correspondence for automorphic sheaves.

Abstract

An intrinsic construction of the tensor category of finite dimensional representations of the Langlands dual group of G in terms of a tensor category of perverse sheaves on the loop group, LG, is given. The construction is applied to the study of the topology of the affine Grassmannian of G and to establishing a Langlands type correspondence for "automorphic" sheaves on the moduli space of G-bundles.