Minimal length elements in a conjugacy class of an affine Weyl group
by Xuhua He
Abstract: Minimal length elements in a conjugacy class of a finite Weyl group were first studied by Geck and Pfeiffer, motivated by a work of Ram on characters of Hecke algebra of type A. They showed that minimal length elements have some remarkable properties. These properties have some applications in representations of Hecke algebras, algebraic groups, finite groups of Lie type, etc. In this talk, we'll discuss an analogy for affine Weyl groups and some application to affine Hecke algebra. It is based on joint works with S. Nie. If time allows, we also discuss some applications to affine Deligne-Lusztig varieties.