Question about the Kauffman knot polynomial

Let L be a link and FL(r,s) the Kauffman knot polynomial for L where r and s are parameters in the Birman-Wenzl-Murakami algebra BWMf(r,s).

Question: is FL(-r,-s) = FL(r,s) for all L?

If the answer is yes, then the link polynomials arising from the vector (fundamental) reprsentations of Uq(-q2n,q) and U-q(q2n,-q) are the same for all L. The answer to the question is yes where L is a link with corresponding braid group element (s1)m for all integers m, but I don’t know the answer for arbitrary L.

One Response to Question about the Kauffman knot polynomial

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