Irreducible projective modules of the Hecke algebras of a finite coxeter group

Abstract

In this paper, we classify the irreducible projective modules, or, equivalently (see, e.g., [6]), the irreducible principal indecomposable modules, of a non-semisimple Hecke algebra H( W, [*), {E @, of a finite Coxeter group W. Let ( W, 3) be a finite Coxeter system [2], and t an indeterminate, q = t*. We denote by H( W, q) the generic Hecke-Iwaho~ algebra [9,2, lo]. This means that H( W, q) is the C(t)-algebra with the basis (T(w)/ WE W> and the multiplication defined by