|Title:||The alternating Hecke algebra and its representations.|
|Authors:||Ratliff, Leah Jane|
|Publisher:||University of Sydney|
Faculty of Science. School of Mathematics and Statistics.
|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.|
|Description:||Doctor of Philosophy|
|Rights and Permissions:||The author retains copyright of this thesis.|
|Type of Work:||PhD Doctorate|
|Appears in Collections:||Sydney Digital Theses (Open Access)|
|01front.pdf||Introduction and Contents etc.||49.94 kB||Adobe PDF|
|02whole.pdf||Main Thesis||469.15 kB||Adobe PDF|
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