A basis for the Birman-Wenzl algebra

H. R. Morton

A basis for the Birman-Wenzl algebra

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arxiv 1012.3116 v1 pith:SRBPSUQK submitted 2010-12-14 math.QA math.RT

H. R. Morton This is my paper

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keywords algebrabirman-wenzlbasisconstructedkauffmanexplicitisomorphismrelations

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An explicit isomorphism is constructed between the Birman-Wenzl algebra, defined algebraically by J. Birman and H. Wenzl using generators and relations, and the Kauffman algebra, constructed geometrically by H. R. Morton and P. Traczyk in terms of tangles. The isomorphism is obtained by constructing an explicit basis in the Birman-Wenzl algebra, analogous to a basis previously constructed for the Kauffman algebra using 'Brauer connectors'. The geometric isotopy arguments for the Kauffman algebra are systematically replaced by algebraic versions using the Birman-Wenzl relations.

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Type B webs give a complete diagrammatic presentation of the subcategory of U_q(so_{2n+1})-representations generated by the fundamental representations.

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