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Fusion-invariant representations for symmetric groups
- Publication Year :
- 2023
-
Abstract
- For a prime $p$, we show that uniqueness of factorization into irreducible $\Sigma_{p^2}$-invariant representations of $\mathbb{Z}/p \wr \mathbb{Z}/p$ holds if and only if $p=2$. We also show nonuniqueness of factorization for $\Sigma_8$-invariant representations of $D_8 \wr \mathbb{Z}/2$. The representation ring of $\Sigma_{p^2}$-invariant representations of $\mathbb{Z}/p \wr \mathbb{Z}/p$ is determined completely when $p$ equals two or three.<br />Comment: 27 pages. Comments are welcome
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2305.17587
- Document Type :
- Working Paper