A construction of Coxeter group representations (II)

An axiomatic approach to the representation theory of Coxeter groups and their Hecke algebras was presented in [R.M. Adin, F. Brenti, Y. Roichman, A unified construction of Coxeter group representations (I), Adv. Appl. Math., in press, arXiv: math.RT/0309364]. Combinatorial aspects of this construction are studied in this paper. In particular, the symmetric group case is investigated in detail. The resulting representations are completely classified and include the irreducible ones.