# 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…

## 44 Citations

Hamiltonian Type Operators in Representations of the Quantum Algebra suq(1,1)

- Mathematics
- 2004

We study some classes of symmetric operators for the discrete series representations of the quantum algebra U_q(su_{1,1}), which may serve as Hamiltonians of various physical systems. The problem of…

Bilinear Generating Functions for Orthogonal Polynomials

- Mathematics
- 1997

Abstract. Using realizations of the positive discrete series representations of the Lie algebra su(1,1) in terms of Meixner—Pollaczek polynomials, the action of su(1,1) on Poisson kernels of these…

Realizations of coupled vectors in the tensor product of representations of su(1, 1) and su(2)

- Mathematics
- 2003

Using the realization of positive discrete series representations of su(1,1) in terms of a complex variable z, we give an explicit expression for coupled basis vectors in the tensor product of v + 1…

Hamiltonian type operators in representations of the quantum algebra Uq(su1,1), e-arXiv: math.QA/0305368

We study some classes of symmetric operators for the discrete series representations of the quantum algebra U q (su 1,1), which may serve as Hamiltonians of various physical systems. The problem of…

BILINEAR GENERATING FUNCTIONSFOR ORTHOGONAL POLYNOMIALS

- 1997

Using realisations of the positive discrete series representations of the Lie algebra su(1; 1) in terms of Meixner-Pollaczek polynomials, the action of su(1; 1) on Poisson kernels of these…

1 2 4 A pr 1 99 7 BILINEAR GENERATING FUNCTIONS FOR ORTHOGONAL POLYNOMIALS

- 2008

Using realisations of the positive discrete series representations of the Lie algebra su(1, 1) in terms of Meixner-Pollaczek polynomials, the action of su(1, 1) on Poisson kernels of these…

Fourier transforms on the quantum SU (1, 1) group

- Mathematics
- 1999

The main goal is to interpret the Askey-Wilson function and the corresponding transform pair on the quantum SU(1,1) group. A weight on the C^*-algebra of continuous functions vanishing at infinity on…

Discrete series representations for sl(2|1), Meixner polynomials and oscillator models

- Mathematics, Physics
- 2012

We explore a model for the one-dimensional quantum oscillator based upon the Lie superalgebra sl(2|1). For this purpose, a class of discrete series representations of sl(2|1) is constructed, each…

Big q-Laguerre and q-Meixner polynomials and representations of the quantum algebra Uq(su1,1)

- Mathematics, Physics
- 2003

Diagonalization of a certain operator in irreducible representations of the positive discrete series of the quantum algebra Uq(su1,1) is studied. Spectrum and eigenfunctions of this operator are…

On suq(1,1)-models of quantum oscillator

- Physics
- 2006

Models of the quantum oscillator, based on the discrete series representations of the quantum algebra suq(1,1), are constructed. The position and momentum operators in these models are twisted…

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