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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On modular Harish-Chandra series of finite unitary groups
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by Emily Norton PDF
Represent. Theory 24 (2020), 483-524 Request permission


In the modular representation theory of finite unitary groups when the characteristic $\ell$ of the ground field is a unitary prime, the $\widehat {\mathfrak {sl}}_e$-crystal on level $2$ Fock spaces graphically describes the Harish-Chandra branching of unipotent representations restricted to the tower of unitary groups. However, how to determine the cuspidal support of an arbitrary unipotent representation has remained an open question. We show that for $\ell$ sufficiently large, the $\mathfrak {sl}_\infty$-crystal on the same level $2$ Fock spaces provides the remaining piece of the puzzle for the full Harish-Chandra branching rule.
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Additional Information
  • Emily Norton
  • Affiliation: Department of Mathematics, TU Kaiserslautern, Gottlieb-Daimler-Strasse 48, 67663 Kaiserslautern, Germany
  • Email:
  • Received by editor(s): November 4, 2019
  • Received by editor(s) in revised form: May 29, 2020
  • Published electronically: October 7, 2020
  • Additional Notes: During the first two weeks of work on this paper, the author was supported by Max Planck Institute for Mathematics, Bonn. The rest of the time the author was supported at TU Kaiserslautern by the grant SFB-TRR 195
  • © Copyright 2020 American Mathematical Society
  • Journal: Represent. Theory 24 (2020), 483-524
  • MSC (2010): Primary 20C33; Secondary 17B65, 05E10, 20C20
  • DOI:
  • MathSciNet review: 4159154