Abstract
The sl(4,R) Lie algebraic treatment of the Winger SU(2) matrices (1959) is extended by analytical continuation to the Bargmann SU(1,1) matrices (1947) corresponding to the positive discrete series irreducible representations. It is then used to obtain an sl(4,R) dynamical potential algebra for the negative-energy solutions of the second Poschl-Teller equations (1933).