Minimal length elements in conjugacy classes of extended affine Weyl group

TL;DR

This paper investigates the properties of minimal length elements within conjugacy classes of extended affine Weyl groups, revealing their special nature and exploring applications to Hecke algebras and loop groups.

Contribution

It characterizes minimal length elements in conjugacy classes of extended affine Weyl groups and discusses their implications for related algebraic structures.

Findings

Minimal length elements are 'special' in the sense of Geck and Pfeiffer.

Applications to extended affine Hecke algebras are discussed.

Implications for loop groups are explored.

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.