Canonical reduced expression for elements of affine Coxeter groups Part I -- Type An
Abstract
We classify the elements of W(An) by giving a canonical reduced expression for each, using basic tools among which affine length. We give some direct consequences for such a canonical form: a description of left multiplication by a simple reflection, a study of the right descent set, and a proof that the affine length is preserved along the tower of affine Coxeter groups of type A, which implies in particular that the corresponding tower of affine Hecke algebras is a faithful tower.
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