Two-rowed Hecke algebra representations at roots of unity

In this paper, we initiate a study into the explicit construction of irreducible representations of the Hecke algebraH_n(q) of typeA_n-1 in the non-generic case whereq is a root of unity. The approach is via the Specht modules ofH_n(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-genericH_n(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.Presented at the 4th International Colloquium Quantum Groups and Integrable Systems, Prague, 22–24 June 1995.