# Combinatorics of $ell,0$-JM partitions, $ell$-cores, the ladder crystal and the finite Hecke algebra - Mathematics > Combinatorics

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Abstract: The following thesis contains results on the combinatorial representationtheory of the finite Hecke algebra $H nq$.In Chapter 2 simple combinatorial descriptions are given which determine whena Specht module corresponding to a partition $\lambda$ is irreducible. This isdone by extending the results of James and Mathas. These descriptions depend onthe crystal of the basic representation of the affine Lie algebra$\widehat{\mathfrak{sl} \ell}$. In Chapter 3 these results are extended todetermine which irreducible modules have a realization as a Specht module. Todo this, a new condition of irreducibility due to Fayers is combined with a newdescription of the crystal from Chapter 2. In Chapter 4 a bijection of coresfirst described by myself and Monica Vazirani is studied in more depth. Variousdescriptions of it are given, relating to the quotient$\widetilde{S \ell}-{S \ell}$ and to the bijection given by Lapointe and Morse.

Autor: Chris Berg

Fuente: https://arxiv.org/