Parabolic character sheaves, III

TL;DR

This paper introduces a new class of character sheaves on ind-varieties associated with loop groups and parahoric subgroups, expanding the geometric representation theory framework.

Contribution

It defines character sheaves on ind-varieties of the form G((t))/U_P, generalizing previous concepts to loop groups and parahoric structures.

Findings

Established a construction of character sheaves on ind-varieties of loop groups.

Extended the theory of character sheaves to new geometric settings.

Provided foundational definitions for future research in geometric representation theory.

Abstract

We define character sheaves on an ind-variety of the form G((t))/U_P where G((t)) is a loop group and U_P is the prounipotent radical of a parahoric subgroup P of G((t)).