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In a finite reflection group, an involution is a product of commuting reflections
I am working through the book Reflection Groups and Coxeter Groups by Humphreys. I got stuck while trying Exercise 1.12.3:
If $w \in W$ is an involution, prove that $w$ can be written as a product of ...
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Are complex reflection groups never perfect?
This is a follow-up to
Conceptual reason why Coxeter groups are never simple
A complex reflection group is a finite subgroup of $ U_n $ that is generated by pseudo reflections. A pseudo reflection is ...
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Angles of the Fundamental Alcove (Chamber?)
I am trying to calculate the angles of the fundamental alcove (chamber?) for the root systems of type $B_2$, $C_2$, and $G_2$; the fundamental alcove (chamber?) forms a triangle in these cases, so I ...
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Reflection Group of Type $D_n$
Here is the description of the reflection group of type $D_n$ in Humphreys' book Reflection Groups and Coxeter Groups:
($D_n$, $n \ge 4)$ Let $V = \Bbb{R}^n$, and define $\Phi$ to be the set of ...
- 8,040
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Reflection Group of Type $C_n$
In Humphreys' book Reflection Groups and Coexeter groups, he defines a group of type $B_n$ (for $n \ge 2$) in the following way:
Let $V = \Bbb{R}^n$, and define $\Phi$ to be the set of all vectors of ...
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