Schur-Weyl duality for $U_{v,t}(sl_{n})$

Abstract

In [8], the authors get a new presentation of two-parameter quantum algebra U v,t (g). Their presentation can cover all Kac-Moody cases. In this paper, we construct a suitable Hopf pairing such that U v,t (sl n ) can be realized as Drinfeld double of certain Hopf subalgebras with respect to the Hopf pairing. Using Hopf pairing, we construct a R-matrix for U v,t (sl n ) which will be used to give the Schur-Weyl dual between U v,t (sl n ) and Hecke algebra H k (v, t). Furthermore, using the Fusion procedure we construct the primitive orthogonal idempotents of H k (v, t). As a corollary, we give the explicit construction of irreducible U v,t (sl n )-representations of V ⊗k .