Mixed quantum skew Howe duality and link invariants of type A

We define a ribbon category Sp(beta), depending on a parameter beta, which encompasses Cautis, Kamnitzer and Morrison's spider category, and describes for beta = m - n the monoidal category of representations of U-q(gl(m vertical bar n)) generated by exterior powers of the vector representation and their duals. We identify this category Sp(beta) with a direct limit of quotients of a dual idempotented quantum group (U) over dot(q) (gl(r+s)), proving a mixed version of skew Howe duality in which exterior powers and their duals appear at the same time. We show that the category Sp(beta) gives a unified natural setting for defining the colored gl(m vertical bar n) link invariant (for beta = m - n) and the colored HOMFLY-PT polynomial (for beta generic). (C) 2018 Elsevier B.V. All rights reserved.