Preprint
The representation theory of somewhere-to-below shuffles
01 Aug 2025
Abstract
The *somewhere-to-below shuffles* are the elements \[ t_{\ell} := \operatorname{cyc}_{\ell}+\operatorname{cyc}_{\ell,\ell+1}+\operatorname{cyc}_{\ell,\ell+1,\ell+2}+\cdots+\operatorname{cyc}_{\ell,\ell+1,\ldots,n} \] (for $\ell \in \{1,2,\dots,n\}$) in the group algebra $\mathbf{k}[S_n]$ of the $n$-th symmetric group $S_n$. Their linear combinations are called the *one-sided cycle shuffles*. We determine the eigenvalues of the action of any one-sided cycle shuffle on any Specht module $\mathcal{S}^λ$ of $S_n$.
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Details
- Title
- The representation theory of somewhere-to-below shuffles
- Creators
- Darij Grinberg
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991022074216104721