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

Korhonen, Mikko

doi:10.1090/proc/14570

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