ON THE Uq(osp(1|2n)) AND U-q(so(2n + 1)) UNCOLORED QUANTUM LINK INVARIANTS

Abstract

Let L be a link and [Formula: see text] 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 [Formula: see text] and [Formula: see text] for each positive integer n and all sufficiently large f, and that [Formula: see text] and [Formula: see text] are identical up to a substitution of variables. For at least one class of links FL(-r, -s) = FL(r, s) implying [Formula: see text] for these links.