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.
| Identifer | oai:union.ndltd.org:ADTP/283345 |
| Date | January 2007 |
| Creators | Ratliff, Leah Jane |
| Publisher | University of Sydney, Faculty of Science. School of Mathematics and Statistics. |
| Source Sets | Australiasian Digital Theses Program |
| Detected Language | English |
| Rights | The author retains copyright of this thesis., http://www.library.usyd.edu.au/copyright.html |
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