On Extending Unipotent Representations to their Stabilizers

TL;DR

This paper proves that irreducible unipotent representations of split Levi subgroups in finite groups of Lie type can be extended to their stabilizers, broadening the understanding of representation extension properties.

Contribution

It extends the multiplicity-freeness theorem from regular embeddings to arbitrary isotypies, enabling the extension of unipotent representations to stabilizers.

Findings

Unipotent representations extend to their stabilizers.

Extended multiplicity-freeness theorem to isotypies.

Broadened understanding of representation extensions in Lie type groups.

Abstract

We show that irreducible unipotent representations of split Levi subgroups of finite groups of Lie type extend to their stabilizers inside the normalizer of the given Levi subgroup. For this purpose, we extend the multiplicity-freeness theorem from regular embeddings to arbitrary isotypies.