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 | References | Similar Articles | Additional Information
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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Additional Information
Olivier Dudas
Affiliation:
UFR de Mathématiques, Bâtiment Sophie Germain, Université Paris Diderot, 75205 Paris CEDEX 13, France
Email:
olivier.dudas@imj-prg.fr
Gunter Malle
Affiliation:
FB Mathematik, TU Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany
Email:
malle@mathematik.uni-kl.de
DOI:
https://doi.org/10.1090/tran/7600
Received by editor(s):
January 20, 2017
Received by editor(s) in revised form:
December 28, 2017
Published electronically:
October 18, 2018
Additional Notes:
The first author gratefully acknowledges financial support by the ANR grant GeRepMod.
The second author gratefully acknowledges financial support by ERC Advanced Grant 291512 and SFB TRR 195
Article copyright:
© Copyright 2018
American Mathematical Society