SPEAKER: Charles Curtis

TITLE: On the Bruhat decomposition and structure constanats of Hecke algebras of finite Chevalley groups.

ABSTRACT The main result is the calculation of the intersection BwB \cap ByB.Bx^{-1}B for w, x, y in the Weyl group, in terms of the root structure. The set was originally used by Iwahori to obtain the structure constants of the Iwahori Hecke algebra. As applications a formula is obtained for the structure constants of the Hecke algebras of Gelfand-Graev repressentations, and a new formula for the polynomials R_{x,y} of Kazhdan and Lusztig.