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The alternating Hecke algebra and its representations.

Doctor of Philosophy / 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.

Identiferoai:union.ndltd.org:ADTP/216146
Date January 2007
CreatorsRatliff, Leah Jane
PublisherUniversity of Sydney, Faculty of Science. School of Mathematics and Statistics.
Source SetsAustraliasian Digital Theses Program
Detected LanguageEnglish
RightsThe author retains copyright of this thesis., http://www.library.usyd.edu.au/copyright.html

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