The characteristic polynomials of imprimitive groups and affine Coxeter groups
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915289708363776 |
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| author | Feng, Chenyue Liu, Shoumin Wang, Xumin |
| author_facet | Feng, Chenyue Liu, Shoumin Wang, Xumin |
| contents | 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 $G(r,p,n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_10788 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The characteristic polynomials of imprimitive groups and affine Coxeter groups Feng, Chenyue Liu, Shoumin Wang, Xumin Representation Theory 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 $G(r,p,n)$. |
| title | The characteristic polynomials of imprimitive groups and affine Coxeter groups |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2505.10788 |