OpenAlex ·
Posh Parking Spaces
- Published
- Source
- OpenAlex
- Published in
- arXiv (Cornell University)
- DOI
- 10.48550/arxiv.2610.07280
- Original
- Read it at the publisher
- Topics
Abstract
Let $W$ be an irreducible complex reflection group with reflection representation $V$. A $W$-stable, faithful homogeneous system of parameters $Θ\subseteq \mathrm{Sym}(V^*)$ of common positive degree $p$ is called a posh hsop; $Θ$ carries a $W$-representation $U$ if $Θ\simeq U$ as ungraded $W$-modules. We classify the posh pairs $(p,U)$ for which a posh hsop of degree $p$ carrying $U$ exists. Every such $U$ is a Galois twist of $V^*$. Extending work of Ito and Okada, we deduce that the quotient $S/(Θ)$ is a permutation module for $W$ if and only if $U \simeq V^*$.
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