Intertwiners of $U'_q\bigl(\widehat{sl}(2)\bigr)$-representations and the vector-valued big $q$-Jacobi transform
Abstract
Linear operators are introduced on tensor products of evaluation modules of obtained from the complementary and strange series representations. The operators satisfy the intertwining condition on finite linear combinations of the canonical basis elements of the tensor products. Infinite sums associated with the action of on six pairs of tensor products are evaluated. For two pairs, the sums are related to the vector-valued big -Jacobi transform of the matrix elements defining the operator . In one case, the sums specify the action of on the irreducible representations present in the decomposition of the underlying indivisible sum of -tensor products. In both cases, bilinear summation formulae for the matrix elements of provide a generalization of the unitarity property.
Keywords
Cite
@article{arxiv.1412.8588,
title = {Intertwiners of $U'_q\bigl(\widehat{sl}(2)\bigr)$-representations and the vector-valued big $q$-Jacobi transform},
author = {R. M. Gade},
journal= {arXiv preprint arXiv:1412.8588},
year = {2015}
}
Comments
72 pages, typos corrected, additional restriction in Proposition 3. The published version contains an additional part at the end of section 5