Unitary representations, branching rules and matrix elements for the non-compact symplectic groups
- 21 April 1985
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 18 (6) , 939-953
- https://doi.org/10.1088/0305-4470/18/6/016
Abstract
The complementarity of the symplectic and orthogonal groups is used to infer properties of the infinite-dimensional unirreps of the former from the character theory of the latter. The complete set of D+-series metaplectic unirreps of Sp(N,R) is identified and branching rules are given for their restrictions to the maximal compact subgroup, U(N), developed in terms of the properties of Schur functions. A known algorithm for the evaluation of matrix elements of the Sp(3,R) Lie algebra is extended to any Sp(N,R) and analytic expressions are given for important classes of unirreps and multiplicity free states.Keywords
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