Symmetric Powers

arxiv（2023）

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摘要

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

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