A classification of affine fully commutative elements

Abstract

We classify fully commutative elements in the affine Coxeter group of type $\widetilde{A_n}$. We give a normal form for such elements, then we propose an application of this normal form: we lift these fully commutative elements to the affine braid group of type $\widetilde{A_n}$ and we get a form for "fully commutative braids".