The Bruhat Order of a Finite Coxeter Group and Elnitsky Tilings
| Autor: | Nicolaides, Robert, Rowley, Peter |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $\mathrm{E}_8$. Comment: Minor updates to pictures and references have now been updated |
| Databáze: | arXiv |
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