Bounding Harish-Chandra series

Dudas, Olivier; Malle, Gunter

doi:10.1090/tran/7600

Bounding Harish-Chandra series
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by Olivier Dudas and Gunter Malle PDF

Trans. Amer. Math. Soc. 371 (2019), 6511-6530 Request permission

Abstract:

We use the progenerator constructed in a previous work 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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