ROOM FOUR: Some Coupled Supersymmetries and Their Associated Bargmann Transforms
In this talk, I will define coupled supersymmetries, discuss the Lie algebras associated to them, and establish eigenvalues of the associated Hamiltonian-like operators from the su(1,1) Lie algebra structure. Due to the Lie-algebraic structure coupled supersymmetries enjoy, Bargmann transforms can be established for some coupled supersymmetries on R. I will develop these for the special classes of supersymmetries given by {1√2(1xn−1ddx+xn),1√2(ddx1xn−1+xn),−1,2n−1}, where n∈N. These Bargmann transforms are associated to holomorphic function spaces and generalize the standard Bargmann transform associated to the (harmonic) oscillator algebra on R.
This is joint work with Bernhard G. Bodmann and Donald J. Kouri. It was supported in part by R. A. Welch Grant E-0608 and in part by NSF grant DMS-1412524.