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

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.