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Title: On homomorphisms between Specht modules for the Ariki-Koike algebra
Author: Corlett, Kelvin
ISNI:       0000 0004 2748 4471
Awarding Body: University of East Anglia
Current Institution: University of East Anglia
Date of Award: 2012
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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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available