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Title: Kazhdan-Lusztig cells in type Bn with unequal parameters
Author: Howse, Edmund
ISNI:       0000 0004 6062 507X
Awarding Body: University of Aberdeen
Current Institution: University of Aberdeen
Date of Award: 2016
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This mathematics thesis deals with combinatorial representation theory. Cells were introduced in a 1979 paper written by D. Kazhdan and G. Lusztig, and have intricate links with many areas of mathematics, including the representation theory of Coxeter groups, Iwahori–Hecke algebras, semisimple complex Lie algebras, reductive algebraic groups and Lie groups. One of the main problems in the theory of cells is their classification for all finite Coxeter groups. This thesis is a detailed study of cells in type Bn with respect to certain choices of parameters, and contributes to the classification by giving the first characterisation of left cells when b/a = n − 1. Other results include the introduction of a generalised version of the enhanced right descent set and exhibiting the asymptotic left cells of type Bn as left Vogan classes. Combinatorial results give rise to efficient algorithms so that cells can be determined with a computer; the methods involved in this work transfer to a new, faster way of calculating the cells with respect to the studied parameters. The appendix is a Python file containing code to make such calculations.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Kazhdan-Lusztig polynomials ; Coxeter groups