Specht modules occupy a position of central importance in the representation theory of
both the symmetric and Iwahori-Hecke algebras, and there is hence considerable interest
in achieving a greater understanding of their structure. To this end, over the past thirty
years there has been much study undertaken of the homomorphism spaces between these
modules, with a particular emphasis being placed upon the construction of explicit homomorphisms
between Specht modules.
Being a generalization of the Iwahori-Hecke algebra of type A, Specht modules are of a
similar importance to the Ariki-Koike algebra. In this thesis we provide and analogue
of James’s kernel intersection theorem, the latter having been a key tool in the study
of homomorphisms between Specht modules in the setting of both the symmetric group
and the Iwahori-Hecke algebra of type A. We also provide and outline of how this result
may be used to construct homomorphisms between Specht modules for the Iwahori-Hecke
algebra of type B. Additionally, as a byproduct of this work, we include a sufficient condition
for certain kinds of commonly encountered tableaux to determine homomorphisms
between analogues of Young’s permutation modules and the Specht modules
