Minimal length elements of extended affine Coxeter groups, II

Abstract

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}.

32 pages

References in corpus (4)

• Minimal length elements in conjugacy classes of extended affine Weyl group
• On certain varieties attached to a Weyl group element
• Minimal length elements of finite Coxeter groups
• $P$-alcoves and nonemptiness of affine Deligne-Lusztig varieties

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• $P$-alcoves and nonemptiness of affine Deligne-Lusztig varieties
• Kottwitz-Rapoport conjecture on unions of affine Deligne-Lusztig varieties
• Mod-$p$ isogeny classes on Shimura varieties with parahoric level structure
• Cocenters and representations of affine $0$-Hecke algebras
• Types and unitary representations of reductive p-adic groups
• Note on affine Deligne-Lusztig varieties
• On the p-adic cohomology of the Lubin-Tate tower
• $P$-alcoves, parabolic subalgebras and cocenters of affine Hecke algebras
• Fundamental elements of an affine Weyl group
• Cordial elements and dimensions of affine Deligne-Lusztig varieties
• Conjugacy classes of non-translations in affine Weyl groups and applications to Hecke algebras
• Cyclically reduced elements in Coxeter groups
• Elements with finite Coxeter part in an affine Weyl group
• Geometric and homological properties of affine Deligne-Lusztig varieties
• Connectedness of affine Deligne-Lusztig varieties for unramified groups
• Newton Strata in Levi Subgroups
• The cocenter-representation duality
• From pro-$p$ Iwahori-Hecke modules to $(\phi ,\Gamma )$-modules, II
• A geometric interpretation of Newton strata
• Affine Deligne-Lusztig varieties via the double Bruhat graph II: Iwahori-Hecke algebra