Eisenstein series and quantum groups

TL;DR

This paper explores the deep connection between geometric Eisenstein series sheaves and the semi-infinite cohomology of small quantum groups, providing a proof of a significant conjecture in the field.

Contribution

It offers a proof of a conjecture linking geometric Eisenstein series sheaves with semi-infinite cohomology of quantum groups, advancing understanding in quantum algebra and geometric representation theory.

Findings

Established the conjectural relationship between Eisenstein series sheaves and quantum group cohomology.

Provided a new proof of the conjecture by [FFKM].

Enhanced the theoretical framework connecting geometric and algebraic aspects of quantum groups.

Abstract

We sketch a proof of a conjecture of [FFKM] that relates the geometric Eisenstein series sheaf with semi-infinite cohomology of the small quantum group with coefficients in the tilting module for the big quantum group.