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Results tagged with coxeter-groups
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user 64444
A Coxeter group is a group defined by a presentation by involutions $r_i$ with relators $(r_ir_j)^{m_{ij}}=1$ for certain family $(m_{ij})$ of integers greater than 1.
3
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answer
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Decompositions of Coxeter groups into trees of groups
In Chapter 8.8 of Davis' "The geometry and topology of Coxeter groups" the smallest class $\mathcal{G}$ of Coxeter groups which contains all spherical Coxeter groups and which is closed under taking a …
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3
votes
1
answer
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Reference request: Finite (multi-parameter) Iwahori-Hecke algebras are pairwise isomorphic
Let $(W,S)$ be a Coxeter system. Let $q=(q_s)_{s\in S} \in \mathbb{R}^{\text{#}S}$ be a tuple of positive real numbers with $q_s=q_t$ whenever $s$ and $t$ are conjugate to each other. Follwing Davis', …
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6
votes
1
answer
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Vanishing of certain coefficients coming from Coxeter groups
Let $\left(W\text{, }S\right)$ be a Coxeter system. For every $w\in W$ let us write $\left|w\right|$ for the length of $w$. Set $\lambda\left(e\right)=1$ where $e\in W$ denotes the neutral element of …
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4
votes
1
answer
127
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Copies of $\mathbb{Z}\oplus \mathbb{F}_2$ in non-affine, irreducible Coxeter groups
Let $\left(W,S\right)$ be a non-affine, irreducible Coxeter system and assume that $W$ contains a copy of $\mathbb{Z}\oplus\mathbb{Z}$ (this is equivalent to $W$ being not word hyperbolic). Does this …
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6
votes
1
answer
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Starting letters of equivalent infinite geodesic paths of hyperbolic Coxeter groups
Let $\left(W\text{, }S\right)$ be a Gromov hyperbolic Coxeter system and denote by $\partial W$ the corresponding Gromov boundary. For $z\in\partial W$ let $\alpha$, $\beta$ be infinite geodesic paths …
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