Whitley, James Ross ORCID: 0000-0002-4117-2410 (2019). Vertices for Iwahori-Hecke algebras of the symmetric group. University of Birmingham. Ph.D.
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Whitley2019PhD.pdf
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Abstract
In this thesis we explore the notions of relative projectivity and vertices for H_n, the Iwahori-Hecke algebra related to the symmetric group. We begin by generalising notions from local representation theory of finite groups, such as a Green correspondence and a Brauer correspondence for the blocks of these algebras. Once this is achieved, we look into further detail about the blocks and specific modules in these blocks, to give a classification of the vertices of blocks of H_n, and use this classification to resolve the Dipper--Du conjecture regarding the structure of vertices of indecomposable H_n-modules. We then apply these results to compute the vertices of some Specht modules, in particular all Specht modules of H_e (where e is the quantum characteristic of H_n), and hook Specht modules when e does not divide n (generalising results from the symmetric group). After considering signed permutation modules to give a method of computing the vertex of signed Young modules, we conclude by looking at possible generalisations of these results to the Iwahori-Hecke algebra of type B.
Type of Work: | Thesis (Doctorates > Ph.D.) | ||||||||||||
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Award Type: | Doctorates > Ph.D. | ||||||||||||
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Licence: | All rights reserved | ||||||||||||
College/Faculty: | Colleges (2008 onwards) > College of Engineering & Physical Sciences | ||||||||||||
School or Department: | School of Mathematics | ||||||||||||
Funders: | Engineering and Physical Sciences Research Council | ||||||||||||
Subjects: | Q Science > QA Mathematics | ||||||||||||
URI: | http://etheses.bham.ac.uk/id/eprint/9470 |
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