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arXiv · 2605.05695

Equivariant version of the characteristic quasi-polynomials of root systems

Ryo Uchiumi
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Abstract

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.

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Ryo Uchiumi. 2026-05-07. Equivariant version of the characteristic quasi-polynomials of root systems. https://arxiv.org/abs/2605.05695

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