We study a mixed tensor product 3⊗m⊗3⊗n of the three-dimensional fundamental
representations of the Hopf algebra Uq​sℓ(2∣1), whenever q is not a
root of unity. Formulas for the decomposition of tensor products of any simple
and projective Uq​sℓ(2∣1)-module with the generating modules
3 and 3 are obtained. The centralizer of
Uq​sℓ(2∣1) on the chain is calculated. It is shown to be the quotient
Xm,n​ of the quantum walled Brauer algebra. The structure of
projective modules over Xm,n​ is written down explicitly. It is
known that the walled Brauer algebras form an infinite tower. We have
calculated the corresponding restriction functors on simple and projective
modules over Xm,n​. This result forms a crucial step in
decomposition of the mixed tensor product as a bimodule over
Xm,n​⊠Uq​sℓ(2∣1). We give an explicit bimodule
structure for all m,n.Comment: 43 pages, 5 figure