SCHUR FUNCTION-ANALYSIS OF THE UNITARY DISCRETE-SERIES REPRESENTATIONS OF THE NONCOMPACT SYMPLECTIC GROUP

We develop and analyse certain character reductions for the infinite-d imensional unitary discrete series representations of the non-compact symplectic group Sp(2n, R). The group reductions considered are Sp(2k, R) superset-of Sp(2, R) x O(k) and the more general Sp(2n k, R) super set-of Sp(2n, R) x O(k). We use Schur function techniques to derive su ccinct formulae involving certain infinite series of Schur functions. The results are relevant to the study of many-body systems with intera ctions of bilinear form and to the description of various quantum phen omena including collective behaviour.