Characters of normalisers of d-split Levi subgroups in Sp2n(q)

TL;DR

This paper parametrizes characters of the normalizer of d-split Levi subgroups in Sp2n(q), using Clifford theory, to support the verification of the inductive Alperin-McKay condition in representation theory.

Contribution

It introduces a parametrization of characters for these normalizers, facilitating progress on the inductive Alperin-McKay condition for symplectic groups.

Findings

Character parametrization of normalizers in Sp2n(q)

Application of Clifford theory in this context

Advancement towards verifying the inductive Alperin-McKay condition

Abstract

In this paper characters of the normaliser of d-split Levi subgroups in Sp2n(q) are parametrised with a particular focus on the Clifford theory between the Levi subgroup and its normaliser. This forms a key step in verifying the inductive Alperin-McKay condition from Sp\"ath via a criterion given by Sp\"ath and the author.