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|dc.contributor.author||Ratliff, Leah Jane||-|
|dc.description||Doctor of Philosophy||en|
|dc.description.abstract||The alternating Hecke algebra is a q-analogue of the alternating subgroups of the finite Coxeter groups. Mitsuhashi has looked at the representation theory in the cases of the Coxeter groups of type A_n, and B_n, and here we provide a general approach that can be applied to any finite Coxeter group.
We give various bases and a generating set for the alternating Hecke algebra. We then use Tits' deformation theorem to prove that, over a large enough field, the alternating Hecke algebra is isomorphic to the group algebra of the corresponding alternating Coxeter group. In particular, there is a bijection between the irreducible representations of the alternating Hecke algebra and the irreducible representations of the alternating subgroup.
In chapter 5 we discuss the branching rules from the Iwahori-Hecke algebra to the alternating Hecke algebra and give criteria that determine these for the Iwahori-Hecke algebras of types A_n, B_n and D_n.
We then look specifically at the alternating Hecke algebra associated to the symmetric group and calculate the values of the irreducible characters on a set of minimal length conjugacy class representatives.||en|
|dc.publisher||University of Sydney||en|
|dc.publisher||Faculty of Science. School of Mathematics and Statistics.||en|
|dc.rights||The author retains copyright of this thesis.||-|
|dc.title||The alternating Hecke algebra and its representations.||en|
|Appears in Collections:||Sydney Digital Theses (Open Access)|
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|01front.pdf||Introduction and Contents etc.||49.94 kB||Adobe PDF|
|02whole.pdf||Main Thesis||469.15 kB||Adobe PDF|
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