Regular Sylow $d$-Tori of classical groups and the McKay conjecture

Britta Spaeth

Regular Sylow $d$-Tori of classical groups and the McKay conjecture

Representation Theory 2009-03-26 v1 Group Theory

Authors: Britta Spaeth

Abstract

We prove for finite reductive groups $G$ of classical type, that every irreducible character of $L$ extends to its inertia group in $N$ , where $L$ is an abelian centraliser of a Sylow $d$ -torus $\mathbf S$ of $G$ and $N:=N_G(\mathbf S)$ . This gives a precise description of the irreducible characters of $N$ . Furthermore it enables us to verify the McKay conjecture in this situation for $G$ and some primes.

Keywords

finite reductive groups Sylow d-torus McKay conjecture irreducible characters classical groups inertia group

Cite

@article{arxiv.0903.4336,
  title  = {Regular Sylow $d$-Tori of classical groups and the McKay conjecture},
  author = {Britta Spaeth},
  journal= {arXiv preprint arXiv:0903.4336},
  year   = {2009}
}

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