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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Jordan blocks of unipotent elements in some irreducible representations of classical groups in good characteristic
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by Mikko Korhonen PDF
Proc. Amer. Math. Soc. 147 (2019), 4205-4219 Request permission

Abstract:

Let $G$ be a classical group with natural module $V$ over an algebraically closed field of good characteristic. For every unipotent element $u$ of $G$, we describe the Jordan block sizes of $u$ on the irreducible $G$-modules which occur as composition factors of $V \otimes V^*$, $\wedge ^2(V)$, and $S^2(V)$. Our description is given in terms of the Jordan block sizes of the tensor square, exterior square, and the symmetric square of $u$, for which recursive formulae are known.
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Additional Information
  • Mikko Korhonen
  • Affiliation: School of Mathematics, The University of Manchester, Manchester M13 9PL, United Kingdom
  • MR Author ID: 1211748
  • Email: korhonen_mikko@hotmail.com
  • Received by editor(s): August 27, 2018
  • Received by editor(s) in revised form: January 19, 2019
  • Published electronically: June 10, 2019
  • Additional Notes: Some of the results in this paper were obtained during the author’s doctoral studies at École Polytechnique Fédérale de Lausanne, supported by a grant from the Swiss National Science Foundation (grant number $200021 \_ 146223$).
  • Communicated by: Pham Huu Tiep
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 4205-4219
  • MSC (2010): Primary 20G05
  • DOI: https://doi.org/10.1090/proc/14570
  • MathSciNet review: 4002536