Filtrations on projective modules for lwahori-Hecke algebras

We consider a generic Iwahori-Hecke algebra H-O associated with a finite Weyl group, defined over a suitable discrete valuation ring O. We define filtrations on H-O-modules in terms of Lusztig's a-function. For a projective module, we show that the quotients of this filtration are direct sums o...