A q-Analog of the Coxeter Complex Original Research Article

In this paper a q-analogue of the Coxeter complex of a finite Coxeter group W is constructed for the (generic) Hecke algebra image 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 remainder of the paper investigates the representations of image afforded by the top homology modules of these complexes. In particular necessary and sufficient conditions are given for a specialisation of the Hecke algebra to decompose into a direct sum of its "truncation" representations.