On homomorphisms between specht modules for the Ariki-Koike algebra

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.

Name dc:type.qualificationname

phd

Level dc:type.qualificationlevel

doctoral

Grantor dc:publisher.institution

University of East Anglia

Year dc:date.issued

2012

Author dc:creator

• Corlett, Kelvin

Language dc:language

en