Formulae relating the Bernstein and Iwahori-Matsumoto presentations of   an affine Hecke algebra
  We give explicit formulae for certain elements occurring in the Bernstein presentation of an affine Hecke algebra, in terms of the usual Iwahori- Matsumoto generators. We utilize certain minimal expressions for said elements and we give a sheaf-theoretic interpretation for the existence of these minimal expressions. 
Thomas J. Haines, Alexandra Pettet