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

摘要

Let L be a link and Phi(A)(L) (q) its link invariant associated with the vector representation of the quantum (super) algebra U-q(A). Let F-L(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 Phi(osp(1 vertical bar 2n))(L) (q) = F-L(-q(2n), q) and Phi(so(2n+ 1))(L)(-q) = F-L(q(2n), -q) for each positive integer n and all sufficiently large f, and that Phi(osp(1 vertical bar 2n))(L)(q) and Phi(so(2n+1))(L)(-q) are identical up to a substitution of variables. For at least one class of links F-L(-r, -s) = F-L(r, s) implying Phi(osp(1 vertical bar 2n))(L) (q) = Phi(so(2n+1))(L)(-q) for these links.