All Questions
4
questions
3
votes
2
answers
208
views
Defining a Coxeter group using all reflections
Let $(W, S)$ be a pair of a group $W$ and a subset $S$ consisting of involutions of $W$. We can consider the group $\tilde W$ with presentation $\langle S | \mathcal{R} \rangle$ where $\mathcal{R}$ ...
- 3,252
4
votes
0
answers
64
views
Computing orders of some irreducible finite Coxeter groups
There is a particular method in Reflection groups and Coxeter groups by Humphreys to compute the orders of various irreducible finite Coxeter groups in Chapter 2.11. The method involves using group ...
- 4,443
7
votes
1
answer
399
views
On groups with presentations $ \langle a,b,c\mid a^2=b^2=c^2=(ab)^p=(bc)^q=(ca)^r=(abc)^s=1\rangle $...
$$
\langle a,b,c\mid a^2=b^2=c^2=(ab)^p=(bc)^q=(ca)^r=1\rangle =\Delta(p,q,r)
$$
This is a presentation of a triangle group $\Delta(p,q,r)$, a special kind of Coxeter group.
EDIT In fact, these are ...
- 18.6k
6
votes
1
answer
376
views
Centralizers of reflections in parabolic subgroups of Coxeter groups
Let us consider a (not necessarily finite) Coxeter group $W$ generated by a finite set of involutions $S=\{s_1,...,s_n\}$ subject (as usual) to the relations $(s_is_j)^{m_{i,j}}$ with $m_{i,j}=m_{j,i}$...
- 2,697