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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

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
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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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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