English

Symmetric Powers

Representation Theory 2023-03-29 v1 Group Theory

Abstract

Given a faithful finite-dimensional representation VV of a finite group GG over any field F\mathbb{F}, we show that any irreducible FG{\mathbb{F}}G-module WW appears, as a submodule or a quotient, in Symm(V)\mathrm{Sym}^m(V) for some integer 1mG1 \leq m \leq |G| (that may depend on WW).

Keywords

Cite

@article{arxiv.2303.15596,
  title  = {Symmetric Powers},
  author = {János Kollár and Pham Huu Tiep},
  journal= {arXiv preprint arXiv:2303.15596},
  year   = {2023}
}
R2 v1 2026-06-28T09:36:48.997Z