%0 Journal Article
%T Minimal length elements of extended affine Coxeter groups, II
%A Xuhua He
%A Sian Nie
%J Mathematics
%D 2011
%I arXiv
%R 10.1112/S0010437X14007349
%X Let $W$ be an extended affine Weyl group. We prove that minimal length elements $w_{\co}$ of any conjugacy class $\co$ of $W$ satisfy some special properties, generalizing results of Geck and Pfeiffer \cite{GP} on finite Weyl groups. We then introduce the "class polynomials" for affine Hecke algebra $H$ and prove that $T_{w_\co}$, where $\co$ runs over all the conjugacy classes of $W$, forms a basis of the cocenter $H/[H, H]$. We also classify the conjugacy classes satisfying a generalization of Lusztig's conjecture \cite{L4}.
%U http://arxiv.org/abs/1112.0824v1