On the Uq(osp(1|2n)) and Uq(so(2n + 1)) uncoloured quantum link invariants

Sacha C. Blumen


Let L be a link and ΦLA(q) its link invariant associated with the vector representation of the quantum (super)algebra Uq(A). Let FL(r,s) be the Kauffman link invariant for L associated with the Birman-Wenzl-Murakami algebra BWMf(r,s) for complex parameters r and s and a sufficiently large rank f. For an arbitrary link L, we show that ΦLosp(1|2n)(q) = FL(−q2n,q) and ΦLso(2n+1)(−q) = FL(q2n,−q) for each positive integer n and all sufficiently large f, and that ΦLosp(1|2n)(q) and ΦLso(2n+1)(−q) are identical up to a substitution of variables. For at least one class of links FL(−r,−s) = FL(r,s)) implying ΦLosp(1|2n)(q) = ΦLso(2n+1)(−q) for these links.

Keywords: Quantum superalgebra, link, Kauffman invariant.

AMS Subject Classification: Primary 57M27; secondary 17B37.

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Wednesday, January 7, 2009