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Jordan blocks of unipotent elements in some irreducible representations of classical groups in good characteristic


Author: Mikko Korhonen
Journal: Proc. Amer. Math. Soc. 147 (2019), 4205-4219
MSC (2010): Primary 20G05
DOI: https://doi.org/10.1090/proc/14570
Published electronically: June 10, 2019
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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
Email: korhonen_mikko@hotmail.com

DOI: https://doi.org/10.1090/proc/14570
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
Article copyright: © Copyright 2019 American Mathematical Society