PreprintCC BY 4.0arXiv
Posh Parking Spaces
Abstract
Let W be an irreducible complex reflection group with reflection representation V. A W-stable, faithful homogeneous system of parameters Θ⊆ Sym(V*) of common positive degree p is called a posh hsop; Θ carries a W-representation U if Θ≃ 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 ≃ V*.
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BibTeX
@misc{stack2026posh,
title = {{Posh Parking Spaces}},
author = {Jason Stack and Nathan Williams},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07280},
eprint = {2610.07280},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07280},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Posh Parking Spaces
AU - Jason Stack
AU - Nathan Williams
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.07280
UR - https://arxiv.org/abs/2610.07280
AB - Let W be an irreducible complex reflection group with reflection representation V. A W-stable, faithful homogeneous system of parameters Θ⊆ Sym(V^*) of common positive degree p is called a posh hsop; Θ carries a W-representation U if Θ≃ 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 ≃ V^*.
ER -