The characteristic polynomials of imprimitive groups and affine Coxeter groups

Chenyue Feng; Shoumin Liu; Xumin Wang

The characteristic polynomials of imprimitive groups and affine Coxeter groups

Representation Theory 2025-05-19 v1

Authors: Chenyue Feng , Shoumin Liu , Xumin Wang

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 $G(r,p,n)$ .

Keywords

characteristic polynomial imprimitive groups affine Coxeter groups finite dimensional representation character

Cite

@article{arxiv.2505.10788,
  title  = {The characteristic polynomials of imprimitive groups and affine Coxeter groups},
  author = {Chenyue Feng and Shoumin Liu and Xumin Wang},
  journal= {arXiv preprint arXiv:2505.10788},
  year   = {2025}
}

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27 pages

The characteristic polynomials of imprimitive groups and affine Coxeter groups

Abstract

Keywords

Cite

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