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research article
Jordan blocks of unipotent elements in some irreducible representations of classical groups in good characteristic
June 19, 2019
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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Type
research article
Authors
Publication date
2019-06-19
Published in
Volume
147
Start page
4205
End page
4219
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
July 8, 2019