Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.19468 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913810265145344 |
|---|---|
| author | Liu, Shoumin Wang, Yuxiang |
| author_facet | Liu, Shoumin Wang, Yuxiang |
| contents | Let $W$ be a finite Coxeter group with Coxeter generating set $S=\{s_1,\ldots,s_n\}$, and $ρ$ be a complex finite dimensional representation of $W$. The characteristic polynomial of $ρ$ is defined as
\begin{equation*}
d(S,ρ)=\det[x_0I+x_1ρ(s_1)+\cdots+x_nρ(s_n)],
\end{equation*}
where $I$ is the identity operator. In this paper, we show the existence of a combinatorics structure within $W$, and thereby prove that for any two complex finite dimensional representations $ρ_1$ and $ρ_2$ of $W$, $d(S,ρ_1)=d(S,ρ_2)$ if and only if $ρ_1 \cong ρ_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19468 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characteristic polynomials and some combinatorics for finite Coxeter groups Liu, Shoumin Wang, Yuxiang Representation Theory Let $W$ be a finite Coxeter group with Coxeter generating set $S=\{s_1,\ldots,s_n\}$, and $ρ$ be a complex finite dimensional representation of $W$. The characteristic polynomial of $ρ$ is defined as \begin{equation*} d(S,ρ)=\det[x_0I+x_1ρ(s_1)+\cdots+x_nρ(s_n)], \end{equation*} where $I$ is the identity operator. In this paper, we show the existence of a combinatorics structure within $W$, and thereby prove that for any two complex finite dimensional representations $ρ_1$ and $ρ_2$ of $W$, $d(S,ρ_1)=d(S,ρ_2)$ if and only if $ρ_1 \cong ρ_2$. |
| title | Characteristic polynomials and some combinatorics for finite Coxeter groups |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2504.19468 |