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arXiv · 2303.15596

Symmetric Powers

János Kollár·Pham Huu Tiep
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Abstract

Given a faithful finite-dimensional representation $V$ of a finite group $G$ over any field $\mathbb{F}$, we show that any irreducible ${\mathbb{F}}G$-module $W$ appears, as a submodule or a quotient, in $\mathrm{Sym}^m(V)$ for some integer $1 \leq m \leq |G|$ (that may depend on $W$).

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János Kollár, Pham Huu Tiep. 2023-03-27. Symmetric Powers. https://arxiv.org/abs/2303.15596

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