Citation
Lu, Daodi (2017) Quasiparabolic Subgroups of Coxeter Groups and Their Hecke Algebra Module Structures. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z9J67DXZ. http://resolver.caltech.edu/CaltechTHESIS:11042016133007537
Abstract
It is well known that the Rpolynomial can be defined for the Hecke algebra of Coxeter groups, and the KazhdanLusztig theory can be developed to understand the representations of Hecke algebra. There is also a generalization for the existence of Rpolynomial and KazhdanLusztig theory for the Hecke algebra module of standard parabolic subgroups of Coxeter groups. In recent work of Rains and Vazirani, a generalization of standard parabolic subgroups, called quasiparabolic subgroups, are introduced, and the corresponding Hecke algebra module is welldefined. However, the existence of the analogous involution (KazhdanLusztig bar operator) on the Hecke algebra module of quasiparabolic subgroups is unknown in general. Assuming the existence of the baroperator, the corresponding Rpolynomials and KazhdanLusztig polynomials can be constructed. We prove the existence of the bar operator for the corresponding Hecke algebra modules of quasiparabolic subgroups in finite classical Coxeter groups with a casebycase verification (Chapter 4). As preparation, we classify all quasiparabolic subgroups of finite classical Coxeter groups. The approach is to first find all rotation subgroups of finite classical Coxeter groups (Chapter 2). Then we exclude the nonquasiparabolic subgroups and confirm the quasiparabolic subgroups (Chapter 3).
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  Coxeter Group, Hecke Algebra, KazhdanLusztig Theory 
Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Mathematics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  31 October 2016 
NonCaltech Author Email:  ludaodi (AT) gmail.com 
Record Number:  CaltechTHESIS:11042016133007537 
Persistent URL:  http://resolver.caltech.edu/CaltechTHESIS:11042016133007537 
DOI:  10.7907/Z9J67DXZ 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  9972 
Collection:  CaltechTHESIS 
Deposited By:  Daodi Lu 
Deposited On:  10 Nov 2016 23:58 
Last Modified:  10 Nov 2016 23:58 
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