Realizations of su(1,1) and Uq(su(1,1)) and generating functions for orthogonal polynomials

@article{Jeugt1998RealizationsOS,
  title={Realizations of su(1,1) and Uq(su(1,1)) and generating functions for orthogonal polynomials},
  author={Joris Van der Jeugt and Ramaswamy Jagannathan},
  journal={Journal of Mathematical Physics},
  year={1998},
  volume={39},
  pages={5062-5078}
}
Positive discrete series representations of the Lie algebra su(1,1) and the quantum algebra Uq(su(1,1)) are considered. The diagonalization of a self-adjoint operator (the Hamiltonian) in these representations and in tensor products of such representations is determined, and the generalized eigenvectors are constructed in terms of orthogonal polynomials. Using simple realizations of su(1,1), Uq(su(1,1)), and their representations, these generalized eigenvectors are shown to coincide with… 

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