On Unipotent Supports of Reductive Groups with a Disconnected Centre

Abstract

Let $G$ be a simple algebraic group defined over a finite field of good characteristic, with associated Frobenius endomorphism $F$. In this article we extend an observation of Lusztig, (which gives a numerical relationship between an ordinary character of $G^F$ and its unipotent support), to the case where $Z(G)$ is disconnected. We then use this observation in some applications to the ordinary character theory of $G^F$.

22 pages; changes from (v3): altered the style of the paper, added proofs for some statements (e.g. Lemma 5.2 and Corollary 7.3), explained in more detail the proof of Theorem 6.2, finally made reference to arXiv:1211.2551 for the proof of Proposition 3.2 instead of the authors thesis

References in corpus (3)

• On Unipotent Supports of Reductive Groups with a Disconnected Centre
• On the Schur indices of cuspidal unipotent characters
• Finding Characters Satisfying a Maximal Condition for Their Unipotent Support

Cited by in corpus (11)

• Action of Automorphisms on Irreducible Characters of Symplectic Groups
• On Unipotent Supports of Reductive Groups with a Disconnected Centre
• Unitriangular Shape of Decomposition Matrices of Unipotent Blocks
• Evaluating Characteristic Functions of Character Sheaves at Unipotent Elements
• Galois Automorphisms and Classical Groups
• The combinatorics of ${\mathrm{GL}}_n$ generalized Gelfand--Graev characters
• Finding Characters Satisfying a Maximal Condition for Their Unipotent Support
• Generalised Gelfand-Graev Representations in Small Characteristics
• Multiplicities in GGGRs for Classical Type Groups with Connected Centre I
• The inductive blockwise Alperin weight condition for type $\mathsf{C}$ and the prime $2$
• Action of automorphisms on irreducible characters of groups of type \textsf{A}