Gould, M.D.Kalnins, Ernie G.2008-10-312008-10-311985-07Gould, M.D. & Kalnins, E.G. (1985). A projection-based solution to the SP(2N) state labeling problem. Journal of Mathematical Physics, 26, 1446.0022-2488https://hdl.handle.net/10289/1223A projection-based solution to the symplectic group state labeling problem is presented. The approach yields a nonorthogonal Gel'fand–Tsetlin basis for the irreducible representations of Sp(2n). A method for evaluating the corresponding overlap coefficients is discussed. The action of the Sp(2n) generators, in the basis obtained, is determined and some matrix element formulas are derived. The results obtained are comparable to the matrix element formulas for O(n) and U(n).application/pdfenCopyright 1985American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in the Journal of Mathematical Physics and may be found at http://jmp.aip.org/jmp/top.jspMathematicsSP groupsirreducible representationsmatricesmatrix elementsO groupsU groupsquantum numberslabellingmultiplicityvectorseigenvaluesunitarityprojection operatorspolynomialscommutation relationsmetricsmatrix algebraalgebraJournal Article10.1063/1.526908