Basic construction of a Coxeter group
= Basic construction of a Coxeter group
{title2=$U(W,K)$}
For a mirrored chamber $K$, the basic construction is
$$
U(W,K)=(W\times K)/\sim,
$$
where $(w,x)\sim(w',x)$ when $w^{-1}w'$ belongs to the subgroup generated by the mirrors containing $x$.