Equivariant version of the characteristic quasi-polynomials of root systems
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866909025247952896 |
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| author | Uchiumi, Ryo |
| author_facet | Uchiumi, Ryo |
| contents | An equivariant characteristic quasi-polynomial is a quasi-polynomial in $q$ consisting of the permutation character on the mod $q$ complement of the corresponding Coxeter arrangement. This concept is a refinement of the conventional characteristic quasi-polynomials of root systems. In this paper, we will show equivariant-theoretic refinements of the some properties of characteristic quasi-polynomials of root systems. Furthermore, we will explicitly compute equivariant characteristic quasi-polynomials of all irreducible reduced root systems and discuss the relationship with root systems constructed by the folding of the extended Dynkin diagrams. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05695 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Equivariant version of the characteristic quasi-polynomials of root systems Uchiumi, Ryo Combinatorics Representation Theory 05E18 (Primary) 17B22 (Secondary) An equivariant characteristic quasi-polynomial is a quasi-polynomial in $q$ consisting of the permutation character on the mod $q$ complement of the corresponding Coxeter arrangement. This concept is a refinement of the conventional characteristic quasi-polynomials of root systems. In this paper, we will show equivariant-theoretic refinements of the some properties of characteristic quasi-polynomials of root systems. Furthermore, we will explicitly compute equivariant characteristic quasi-polynomials of all irreducible reduced root systems and discuss the relationship with root systems constructed by the folding of the extended Dynkin diagrams. |
| title | Equivariant version of the characteristic quasi-polynomials of root systems |
| topic | Combinatorics Representation Theory 05E18 (Primary) 17B22 (Secondary) |
| url | https://arxiv.org/abs/2605.05695 |