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arXiv · 2409.01084

The quasi-polynomiality of mod q permutation representation for a linear finite group action on a lattice

Ryo Uchiumi·Masahiko Yoshinaga
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Abstract

For given linear action of a finite group on a lattice and a positive integer q, we prove that the mod q permutation representation is a quasi-polynomial in q. Additionally, we establish several results that can be considered as mod q-analogues of results by Stapledon for equivariant Ehrhart quasi-polynomials. We also prove a reciprocity-type result for multiplicities of irreducible decompositions.

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Ryo Uchiumi, Masahiko Yoshinaga. 2024-09-02. The quasi-polynomiality of mod q permutation representation for a linear finite group action on a lattice. https://arxiv.org/abs/2409.01084

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