We study a mixed tensor product 3⊗m⊗3⊗n of the three-dimensional fundamental
representations of the Hopf algebra Uqsℓ(2∣1), whenever q is not a
root of unity. Formulas for the decomposition of tensor products of any simple
and projective Uqsℓ(2∣1)-module with the generating modules
3 and 3 are obtained. The centralizer of
Uqsℓ(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⊠Uqsℓ(2∣1). We give an explicit bimodule
structure for all m,n.Comment: 43 pages, 5 figure