The Cyclotomic Birman-Murakami-Wenzl Algebras

Abstract

----- Please see the pdf file for the actual abstract and important remarks, which could not be put here due to the arXiv length restrictions. ----- This thesis presents a study of the cyclotomic BMW (Birman-Murakami-Wenzl) algebras, introduced by Haring-Oldenburg as a generalization of the BMW algebras associated with the cyclotomic Hecke algebras of type G(k,1,n) (also known as Ariki-Koike algebras) and type B knot theory involving affine/cylindrical tangles. They are shown to be free of rank k^n (2n-1)!! and to have a topological realization as a certain cylindrical analogue of the Kauffman Tangle algebra. Furthermore, the cyclotomic BMW algebras are proven to be cellular, in the sense of Graham and Lehrer. This Ph.D. thesis, completed at the University of Sydney, was submitted September 2007 and passed December 2007.

93 pages, including 2 pages for newly added abstract; University of Sydney - Ph.D. thesis, submitted Sept 2007, passed Dec 2007. (Note: Apologies for any awkward spacing or formatting caused by the change from a4 sized paper to the default letter sized paper on arXiv; please email for the original a4 paper version)

References in corpus (3)

• Specht modules and semisimplicity criteria for Brauer and Birman--Murakami--Wenzl Algebras
• Affine braids, Markov traces and the category O
• Gram determinants and semisimplity criteria for Birman-Wenzl algebras

Cited by in corpus (20)

• On the freeness of the cyclotomic BMW algebras: admissibility and an isomorphism with the cyclotomic Kauffman tangle algebras
• Remarks on Cyclotomic and Degenerate Cyclotomic BMW Algebras
• The representation theory of cyclotomic BMW algebras
• Affine and degenerate affine BMW algebras: The center
• The representations of cyclotomic BMW algebras
• Cyclotomic Birman--Wenzl--Murakami algebras, II: Admissibility Relations and Freeness
• The cyclotomic BMW algebra associated with the two string type B braid group
• Flat connections and Brauer Type Algebras
• Birman-Murakami-Wenzl algebras for general Coxeter groups
• Cellularity of Cyclotomic Birman--Wenzl--Murakami algebras
• A basis theorem for the affine Kauffmann category and its cyclotomic quotients
• On geometrically defined extensions of the Temperley-Lieb category in the Brauer category
• Handlebody diagram algebras
• Decomposition numbers for the cyclotomic Brauer algebras in characteristic zero
• Affine cellularity of affine Birman-Murakami-Wenzl algebras
• An algebraic view of bacterial genome evolution
• Cyclotomic Birman--Wenzl--Murakami algebras, I: Freeness and realization as tangle algebras
• Comparison of Admissibility Conditions for Cyclotomic Birman--Wenzl--Murakami Algebras
• Singular parameters for the Birman-Murakami-Wenzl algebra
• Fusion procedure for cyclotomic BMW algebras