Inductive basis on Birman-Murakami-Wenzl algebras and (transverse) Markov traces

Loïc Poulain d'Andecy; Anne-Laure Thiel; Emmanuel Wagner

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arXiv · 1711.08670

Inductive basis on Birman-Murakami-Wenzl algebras and (transverse) Markov traces

Loïc Poulain d'Andecy·Anne-Laure Thiel·Emmanuel Wagner

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Abstract

We construct a new inductive basis of the Birman-Murakami-Wenzl algebra. Using it, we provide a new proof of the existence of the Markov trace on the BMW algebras affording the two-variable Kauffman polynomial. We prove also that all the transverse Markov traces on the BMW algebras are determined by the self-linking number, the HOMFLY-PT polynomial and the two-variable Kauffman polynomial.

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Loïc Poulain d'Andecy, Anne-Laure Thiel, Emmanuel Wagner. 2017-11-23. Inductive basis on Birman-Murakami-Wenzl algebras and (transverse) Markov traces. https://arxiv.org/abs/1711.08670

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