Realizations of coupled vectors in the tensor product of representations of su(1,1) and su(2)

[摘要] Using the realization of positive discrete series representations of su(1, 1) in terms of a complex variable z, we give an explicit expression for coupled basis vectors in the tensor product of v + 1 representations as polynomials in v + 1 variables z(1),...,z(v+1). These expressions use the terminology of binary coupling trees (describing the coupled basis vectors), and are explicit in the sense that there is no reference to the Clebsch-Gordan coefficients of su(1, 1). In general, these polynomials can be written as (terminating) multiple hypergeometric series. For v = 2, these polynomials are triple hypergeometric series, and a relation between the two binary coupling trees yields a relation between two triple hypergeometric series. The case of su(2) is discussed next. Also here the polynomials are determined explicitly in terms of a known realization; they yield an efficient way of computing coupled basis vectors in terms of uncoupled basis vectors. (C) 2003 Elsevier B.V. All rights reserved.

[发布日期] 2003-11-01

[效力级别]  Proceedings Paper

[关键词] multiple hypergeometric series;tensor products;realizations;coupling coefficient