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

Author: Levaillant, Claire Isabelle

Year: 2008

Degree: Dissertation (Ph.D.)

Advisor: Wales, David B.

Committee Members: Wales, David B.; Ku, Cheng Yeaw; Ramakrishnan, Dinakar; Wilson, Richard M.

Option: Mathematics

DOI: 10.7907/2PFP-HG33

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.

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