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arXiv · 1701.01260

Bounding Harish-Chandra series

Olivier Dudas·Gunter Malle
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Abstract

We use the progenerator constructed in our previous paper to give a necessary condition for a simple module of a finite reductive group to be cuspidal, or more generally to obtain information on which Harish-Chandra series it can lie in. As a first application we show the irreducibility of the smallest unipotent character in any Harish-Chandra series. Secondly, we determine a unitriangular approximation to part of the unipotent decomposition matrix of finite orthogonal groups and prove a gap result on certain Brauer character degrees.

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Olivier Dudas, Gunter Malle. 2017-01-05. Bounding Harish-Chandra series. https://arxiv.org/abs/1701.01260

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