Two-rowed Hecke algebra representations at roots of unity

Abstract

In this paper, we initiate a study into the explicit construction of irreducible representations of the Hecke algebra Hn(q) of type An-1 in the non-generic case where q is a root of unity. The approach is via the Specht modules of Hn(q) which are irreducible in the generic case, and possess a natural basis indexed by Young tableaux. The general framework in which the irreducible non-generic Hn(q)-modules are to be constructed is set up and, in particular, the full set of modules corresponding to two-part partitions is described. Plentiful examples are given.