Intertwiners of U'q(sl(2))-representations and the vector-valued big q-Jacobi transform

Gade, R. M.
September 2014
Journal of Mathematical Physics;2014, Vol. 55 Issue 9, p1
Academic Journal
Linear operators R are introduced on tensor products of evaluation modules of U'q(sl(2)) obtained from the complementary and strange series representations. The operators R satisfy the intertwining condition on finite linear combinations of the canonical basis elements of the tensor products. Infinite sums associated with the action of R on six pairs of tensor products are evaluated. For two pairs, the sums are related to the vector-valued big q-Jacobi transform of the matrix elements defining the operator R. In one case, the sums specify the action of R on the irreducible representations present in the decomposition of the underlying indivisible sum of U'q(sl(2))-tensor products. In both cases, bilinear summation formulae for the matrix elements of R provide a generalization of the unitarity property. Corresponding results are given for the remaining pairs.


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