Combinatorics of (l, 0)-JM partitions, l-cores, the ladder crystal and the finite Hecke algebra

The following thesis contains results on the combinatorial representation theory of the finite Hecke algebra Hn( q).;In Chapter 2 simple combinatorial descriptions are given which determine when a Specht module corresponding to a partition lambda is irreducible. This is done by extending the results of James and Mathas. These descriptions depend on the crystal of the basic representation of the affine Lie algebra slℓ&d14; .;In Chapter 3 these results are extended to determine which irreducible modules have a realization as a Specht module. To do this, a new condition of irreducibility due to Fayers is combined with a new description of the crystal from Chapter 2.;In Chapter 4 a bijection of cores first described by myself and Monica Vazirani is studied in more depth. Various descriptions of it are given, relating to the quotient S˜ℓ/Sℓ and to the bijection given by Lapointe and Morse.