Irreducibility of the Lawrence-Krammer Representation of the BMW Algebra of Type An-1

Citation

Levaillant, Claire Isabelle (2008) Irreducibility of the Lawrence-Krammer Representation of the BMW Algebra of Type An-1. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/2PFP-HG33. https://resolver.caltech.edu/CaltechETD:etd-05292008-110016

Abstract

We show that the Lawrence-Krammer representation of the BMW algebra of type An-1 over the field Q(l,r) is generically irreducible, but that for some values of the parameters l and r, when these are specialized in the field of complex numbers, it becomes reducible. When the representation is reducible, we describe the invariant subspaces by giving their dimension and some spanning vectors.

Item Type:	Thesis (Dissertation (Ph.D.))
Subject Keywords:	BMW algebras; representation theory
Degree Grantor:	California Institute of Technology
Division:	Physics, Mathematics and Astronomy
Major Option:	Mathematics
Thesis Availability:	Public (worldwide access)
Research Advisor(s):	Wales, David B.
Thesis Committee:	Wales, David B. (chair) Ku, Cheng Yeaw Ramakrishnan, Dinakar Wilson, Richard M.
Defense Date:	1 May 2008
Non-Caltech Author Email:	clairelevaillant (AT) yahoo.fr
Record Number:	CaltechETD:etd-05292008-110016
Persistent URL:	https://resolver.caltech.edu/CaltechETD:etd-05292008-110016
DOI:	10.7907/2PFP-HG33
Default Usage Policy:	No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:	2255
Collection:	CaltechTHESIS
Deposited By:	Imported from ETD-db
Deposited On:	30 Jul 2008
Last Modified:	03 Dec 2019 22:30

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