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arxiv 2303.15596 v1 pith:52YOZZOB submitted 2023-03-27 math.RT math.GR

János Kollár , Pham Huu Tiep This is my paper · ORCID
classification math.RTmath.GR
keywords mathbbappearsdependfaithfulfieldfinitefinite-dimensionalgiven
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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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Cited by 1 Pith paper

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  1. Adaptive Symmetry Discovery for Dynamical System Identification

    cs.LG 2026-08 reject novelty 7.0 of 10

    For feature-lifted dynamical systems with unknown finite-group symmetry, the paper proves a representation-theoretic characterization of the minimal identification trajectory length and gives a random-generator algori...

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