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Jordan blocks of nilpotent elements in some irreducible representations of classical groups in good characteristic
- Source :
- J. Pure Appl. Algebra 225 (2021), no. 8, 106694, 10 pp
- Publication Year :
- 2020
-
Abstract
- Let $G$ be a classical group with natural module $V$ and Lie algebra $\mathfrak{g}$ over an algebraically closed field $K$ of good characteristic. For rational irreducible representations $f: G \rightarrow \operatorname{GL}(W)$ occurring as composition factors of $V \otimes V^*$, $\wedge^2(V)$, and $S^2(V)$, we describe the Jordan normal form of $\mathrm{d} f(e)$ for all nilpotent elements $e \in \mathfrak{g}$. The description is given in terms of the Jordan block sizes of the action of $e$ on $V \otimes V^*$, $\wedge^2(V)$, and $S^2(V)$, for which recursive formulae are known. Our results are in analogue to earlier work (Proc. Amer. Math. Soc., 147 (2019) 4205-4219), where we considered these same representations and described the Jordan normal form of $f(u)$ for every unipotent element $u \in G$.<br />Comment: to appear in J. Pure Appl. Algebra
- Subjects :
- Mathematics - Group Theory
Mathematics - Representation Theory
20G05
Subjects
Details
- Database :
- arXiv
- Journal :
- J. Pure Appl. Algebra 225 (2021), no. 8, 106694, 10 pp
- Publication Type :
- Report
- Accession number :
- edsarx.2010.16173
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.jpaa.2021.106694