On a finite type property of certain affine Deligne-Lusztig varieties

Abstract

We give a new proof of the fact that affine Deligne-Lusztig varieties for an algebraic group of adjoint type, associated with superbasic elements, are of finite type. The proof uses a property of the associated Hecke algebra, which we reprove, and an estimate of the length of certain elements in the affine Weyl group.