For the notations I am using, I refer to the Appendix at the end of this post. Here is what, for the sake of this post, I consider to be Reifegerste's theorem: Theorem 1. Let $n\in\mathbb N$ and ...
The hyperoctahedral group $H_n$ has several descriptions; as a wreath product; as signed permutation matrices; as the Weyl group of type $B_n$ or $C_n$. In all these descriptions it is apparent that ...