Canonical reduced expression in affine Coxeter groups of type ${\tilde{A}}_n$, ${\tilde{B}}_n$, ${\tilde{D}}_n$

Sadek Al Harbat

We classify the elements of $W({\tilde{A}}_n)$ by giving a canonical reduced expression for each, using basic tools among which affine length. We give some direct consequences for su…