Affine Quantum Super Schur-Weyl Duality

The Schur-Weyl duality, which started as the study of the commuting actions of the symmetric group S_d and GL(n, ℂ) on V^⊗d where V = ℂⁿ, was extended by Drinfeld and Jimbo to the context of the finite Iwahori-Hecke algebra H_d(q²) and quantum algebras U_q(gl(n)), on using universal R-matrices, which solve the Yang-Baxter equation. There were two extensions of this duality in the Hecke-quantum case: to the affine case, by Chari and Pressley, and to the super case, by Moon and by Mitsuhashi. We complete this chain of works by completing the cube, dealing with the general affine super case, relating the commuting actions of the affine Iwahori-Hecke algebra Hda(q2) and of the affine quantum Lie superalgebra Uq,aσ(sl(m,n)) using the presentation by Yamane in terms of generators and relations, acting on the d th tensor power of the superspace V = ℂ^{m + n}. Thus we construct a functor and show it is an equivalence of categories of Hda(q2) and Uq,aσ(sl(m,n))-modules when d < n^′ = m + n.