Character sheaves on loop Lie algebras: polar partition

TL;DR

This paper introduces a polar partition of loop Lie algebras inspired by supercuspidal representation theory, aiming to develop a conjectural framework for character sheaves on these algebras.

Contribution

It proposes a novel polar partition of loop Lie algebras and connects it to the construction of character sheaves, extending ideas from supercuspidal representations.

Findings

Partition of loop Lie algebras into invariant sets

Motivated by supercuspidal representation construction

Conjectural approach to character sheaves

Abstract

In this paper we propose a partition of loop Lie algebras into invariant sets parametrized by polar data. Our polar partition is motivated by J-K. Yu's construction of supercuspidal representations and leads to a conjectural construction of character sheaves on loop Lie algebras.