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arXiv · 2505.10788

The characteristic polynomials of imprimitive groups and affine Coxeter groups

Chenyue Feng·Shoumin Liu·Xumin Wang
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Abstract

In this paper, we will seek appropriate generators to define the characteristic polynomials of $G(r,1,n)$, and prove that for every finite dimensional representation of $G(r,1,n)$, the characteristic polynomial of $G(r,1,n)$ determines the character of this representation. Furthermore, the same conclusion holds for affine Coxeter groups \(\widetilde{W}\) and $G(r,p,n)$.

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BibTeXRIS

Chenyue Feng, Shoumin Liu, Xumin Wang. 2025-05-16. The characteristic polynomials of imprimitive groups and affine Coxeter groups. https://arxiv.org/abs/2505.10788

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