The Bruhat Order of a Finite Coxeter Group and Elnitsky Tilings
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914879319834624 |
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| author | Nicolaides, Robert Rowley, Peter |
| author_facet | Nicolaides, Robert Rowley, Peter |
| contents | Suppose that $W$ is a finite Coxeter group and $W_J$ a standard parabolic subgroup of $W$. The main result proved here is that for any for any $w \in W$ and reduced expression of $w$ there is an Elnitsky tiling of a $2m$-polygon, where $m = [W : W_J]$. The proof is constructive and draws together the work on E-embedding in \cite{nicolaidesrowley1} and the deletion order in \cite{nicolaidesrowley3}. Computer programs which produce such tilings may be downloaded from \cite{github} and here we also present examples of the tilings for, among other Coxeter groups, the exceptional Coxeter group $\mathrm{E}_8$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07975 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Bruhat Order of a Finite Coxeter Group and Elnitsky Tilings Nicolaides, Robert Rowley, Peter Group Theory Suppose that $W$ is a finite Coxeter group and $W_J$ a standard parabolic subgroup of $W$. The main result proved here is that for any for any $w \in W$ and reduced expression of $w$ there is an Elnitsky tiling of a $2m$-polygon, where $m = [W : W_J]$. The proof is constructive and draws together the work on E-embedding in \cite{nicolaidesrowley1} and the deletion order in \cite{nicolaidesrowley3}. Computer programs which produce such tilings may be downloaded from \cite{github} and here we also present examples of the tilings for, among other Coxeter groups, the exceptional Coxeter group $\mathrm{E}_8$. |
| title | The Bruhat Order of a Finite Coxeter Group and Elnitsky Tilings |
| topic | Group Theory |
| url | https://arxiv.org/abs/2407.07975 |