The quasi-polynomiality of mod q permutation representation for a linear finite group action on a lattice
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916377443434496 |
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| author | Uchiumi, Ryo Yoshinaga, Masahiko |
| author_facet | Uchiumi, Ryo Yoshinaga, Masahiko |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01084 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The quasi-polynomiality of mod q permutation representation for a linear finite group action on a lattice Uchiumi, Ryo Yoshinaga, Masahiko Combinatorics Representation Theory 05E18, 20C10 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. |
| title | The quasi-polynomiality of mod q permutation representation for a linear finite group action on a lattice |
| topic | Combinatorics Representation Theory 05E18, 20C10 |
| url | https://arxiv.org/abs/2409.01084 |