A Q-ANALOG OF THE COXETER COMPLEX

In this paper a q-analogue of the Coxeter complex of a finite Coxeter group W is constructed for the (generic) Hecke algebra H associated to W. It is shown that the homology of this chain complex, together with that of its truncations, vanishes away from top dimension. The remain der of the paper investigates the representations of Y afforded by the top homology modules of these complexes. In particular necessary and sufficient conditions are given for a specialisation of the Hecke alge bra to decompose into a direct sum of its ''truncation'' representatio ns. (C) 1994 Academic Press, Inc.