Tensor products of q-superalgebra representations and q-series identities

Won Sang Chung, E. G. Kalnins, W. Miller

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We work out examples of tensor products for distinct q-generalizations of Euclidean, oscillator and sℓ(2) type superalgebras in cases where the method of highest-weight vectors will not apply. In particular, we use the three-term recurrence relations for Askey-Wilson polynomials to decompose the tensor product of representations from the positive discrete series and representations from the negative discrete series. We show that various q-analogues of the exponential function can be used to mimic the exponential mapping from a Lie algebra to its Lie group and we compute the corresponding matrix elements of the 'group operators' on these representation spaces. We show that the matrix elements themselves transform irreducibly under the action of the quantum superalgebra. The most important q-series identities derived here are interpreted as the expansion of the matrix elements of a 'group operator' (via the exponential mapping) in a tensor product basis in terms of the matrix elements in a reduced basis They involve q-hypergeometric series with base -q, 0 < q < 1.

Original languageEnglish (US)
Pages (from-to)7147-7166
Number of pages20
JournalJournal of Physics A: Mathematical and General
Issue number20
StatePublished - Oct 21 1997
Externally publishedYes


Dive into the research topics of 'Tensor products of q-superalgebra representations and q-series identities'. Together they form a unique fingerprint.

Cite this