On Unipotent Supports of Reductive Groups with a Disconnected Centre

Details On Unipotent Supports of Reductive Groups with a Disconnected Centre On Unipotent Supports of Reductive Groups with a Disconnected Centre

2011-08-24

arxiv.org/abs/1108.4814v3

Mathematics

Representation Theory

23 pages; changes from (v2): improved the proof of Lemma 2.2, removed superfluous arguments from section 2, clarified the choi

Scientific paper

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 $G^F$.

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