Height 0 characters of finite groups of Lie type

By Gunter Malle. 2007

132 citations recorded by the source corpus.

We give a classification of irreducible characters of finite groups of Lie type of p′-degree, where p is any prime different form the defining characteristic, in terms of local data. More precisely, we give a classification in terms of data related to the normalizer of a suitable Levi subgroup, which in many cases coincides with the normalizer of a Sylow p-subgroup. The McKayconjecture asserts that there exists a bijection between characters of p′-degree of a group and of the normalizer of a Sylow p-subgroup. We hope that our result will constitute a major step towards a proof of this conjecture for groups of Lie type, and, in conjunction with a recent reduction result of Isaacs, Malle and Navarro, for arbitrary finite groups.

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a4efccd8a3cfc90e05644df2c81743768195b971

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In Artificial Intelligence

In Discrete Mathematics and Combinatorics

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Citations in the corpus

A reduction theorem for the McKay conjecture (2007, background): “(See the work of Malle [14] and B.”
On the inductive Alperin–McKay and Alperin weight conjecture for groups with abelian Sylow subgroups (2014, methodology): “9 that an (AM)-bijection exists if all characters of suitable local subgroups extend, similar to the case considered in [22].”
Characters of odd degree (2015, methodology): “In accordance with [Mal07] we choose N to be the nor-maliser of a suitable Sylow d -torus.”