Bounding Harish-Chandra series

Dudas, Olivier; Malle, Gunter

doi:10.1090/tran/7600

Bounding Harish-Chandra series

Authors: Olivier Dudas and Gunter Malle
Journal: Trans. Amer. Math. Soc. 371 (2019), 6511-6530
MSC (2010): Primary 20C33; Secondary 20C08
DOI: https://doi.org/10.1090/tran/7600
Published electronically: October 18, 2018
MathSciNet review: 3937335
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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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