A Q{analogue of the Coxeter Complex
نویسنده
چکیده
In this paper a q{analogue of the Coxeter complex of a nite 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 remainder of the paper investigates the representations of H aaorded by the top homology modules of these complexes. In particular necessary and suucient conditions are given for a specialisation of the Hecke algebra to decompose into a direct sum of its \truncation" representations.
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