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Results tagged with coxeter-groups
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user 20595
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.
16
votes
Is {6,3,7} an 'ultrahyperbolic' Coxeter group?
Actually, every Coxeter system of rank four is either euclidean or hyperbolic. That is, the canonical bilinear form has at most one negative eigenvalue.
It follows from the paper Sphere packings and …
- 2,581
7
votes
2
answers
440
views
Are there infinitely many commensurable classes of finite-covolume hyperbolic Coxeter groups?
Allcock(2006) proved that
there are infinitely many finite-covolume (resp. cocompact) Coxeter groups acting on hyperbolic space $H^n$ for every $n\le 19$ (resp. $n\le 6$).
His main technique of …
- 2,581
3
votes
1
answer
549
views
Eigenvalues for elements of (infinite) Coxeter groups
My current research requires some knowledge on the eigenvectors of elements (of infinite order) of Coxeter groups view as reflections in their geometric representation.
After some reading, my impres …
- 2,581