Minimal length elements in conjugacy classes of extended affine Weyl group

Abstract

We study the minimal length elements in an integral conjugacy class of a classical extended affine Weyl group and we show that these elements are quite "special" in the sense of Geck and Pfeiffer \cite{GP93}. We also discuss some application on extended affine Hecke algebras and loop groups.

References in corpus (4)

• Truncations of level 1 of elements in the loop group of a reductive group
• On Some Stratifications of Affine Deligne-Lusztig Varieties for SL_3
• On some partitions of a flag manifold
• Dimensions of affine Deligne-Lusztig varieties in affine flag varieties

Cited by in corpus (12)

• Minimal length elements of extended affine Coxeter groups, II
• Hecke algebras and $p$-adic groups
• Cocenters and representations of affine $0$-Hecke algebras
• Note on affine Deligne-Lusztig varieties
• Closure of Steinberg fibers and affine Deligne-Lusztig varieties
• Geometric and homological properties of affine Deligne-Lusztig varieties
• Dimensions of affine Deligne-Lusztig varieties in affine flag varieties
• The cocenter-representation duality
• Connectedness of affine Deligne-Lusztig varieties for unramified groups
• Stratifications in the reduction of Shimura varieties
• Cocenters and representations of pro-$p$ Hecke algebras
• Notes on partial conjugation