A note on tensor products of \(q\)-algebra representations and orthogonal polynomials (Q1919450)

The authors have given examples of tensor products of distinct generalized \(Sl_q(2)\) algebras with a factor from the positive discrete series of representations of one algebra and a factor from the negative discrete series of the other. The authors have also shown the equation for the common eigenfunctions of the Casimir operator and the Cartan subalgebra generator is a three term recurrence relation corresponding to orthogonality for special cases of the Askey-Wilson polynomials and this connection yields a resolution of the tensor product representation into a direct integral of irreducible representation. Further, an identity for the matrix elements of the ``group representation operators'' with respect to the tensor product and the reduced bases follows easily has also been studied.