Extended Affine Weyl groups, the Baum-Connes correspondence and Langlands duality

TL;DR

This paper explores the connection between the Baum-Connes conjecture, Langlands duality, and affine Weyl groups, revealing that the Baum-Connes correspondence for these groups is derived from Langlands duality.

Contribution

It demonstrates that the Baum-Connes correspondence for affine and extended affine Weyl groups originates from Langlands duality for the underlying Lie group.

Findings

Baum-Connes correspondence for affine Weyl groups is linked to Langlands duality.

The work establishes a conceptual bridge between geometric group theory and Langlands program.

Provides new insights into the structure of extended affine Weyl groups in relation to duality principles.

Abstract

In this paper we consider the Baum-Connes correspondence for the affine and extended affine Weyl groups of a compact connected semisimple Lie group. We show that the Baum-Connes correspondence in this context arises from Langlands duality for the Lie group.