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

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 $V\otimes V^{\ast }$, ${\wedge }^2(V)$, 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.

arXiv commentto appear in Proc. Amer. Math. Soc

References in corpus (1)

• Exterior and Symmetric Powers of Modules for Cyclic 2-Groups

Cited by in corpus (4)

• A proof of {Gross}' conjecture on $2$-automorphic $2$-groups
• Hesselink normal forms of unipotent elements in some representations of classical groups in characteristic two
• Jordan blocks of nilpotent elements in some irreducible representations of classical groups in good characteristic
• Adjoint Jordan blocks for simple algebraic groups of type $C_{\ell }$ in characteristic two