On $e$-cuspidal pairs of finite groups of exceptional Lie Type

Ruwen Hollenbach

On $e$-cuspidal pairs of finite groups of exceptional Lie Type

Representation Theory 2021-02-17 v2

Authors: Ruwen Hollenbach

Abstract

Let $G$ be a simple, simply connected algebraic group of exceptional type defined over $\mathbb{F}_q$ with Frobenius endomorphism $F: G \to G$ . Let $\ell \nmid q$ be a good prime for $G$ . We determine the number of irreducible Brauer characters in the quasi-isolated $\ell$ -blocks of $G^F$ . This is done by proving that generalized $e$ -Harish-Chandra theory holds for the Lusztig series associated to quasi-isolated elements of $G^{*F}$ .

Keywords

exceptional lie type e-cuspidal pairs brauer characters quasi-isolated blocks lusztig series harish-chandra theory

Cite

@article{arxiv.1905.10754,
  title  = {On $e$-cuspidal pairs of finite groups of exceptional Lie Type},
  author = {Ruwen Hollenbach},
  journal= {arXiv preprint arXiv:1905.10754},
  year   = {2021}
}

Comments

Rewritten using new results of Geck-Malle, fixed mistakes and added more information in the tables

On $e$-cuspidal pairs of finite groups of exceptional Lie Type

Abstract

Keywords

Cite

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