Realizations of $su(1,1)$ and $U_q(su(1,1))$ and generating functions for orthogonal polynomials
Van der Jeugt, J. ; Jagannathan, R.
arXiv, 9807019 / Harvested from arXiv
Text on arXiv
Positive discrete series representations of the Lie algebra $su(1,1)$ and the quantum algebra $U_q(su(1,1))$ 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 $su(1,1)$, $U_q(su(1,1))$, and their representations, these generalized eigenvectors are shown to coincide with generating functions for orthogonal polynomials. The relations valid in the tensor product representations then give rise to new generating functions for orthogonal polynomials, or to Poisson kernels. In particular, a group theoretical derivation of the Poisson kernel for Meixner-Pollaczak and Al-Salam--Chihara polynomials is obtained.
Publié le : 1998-07-20
Classification:  Mathematical Physics,  Mathematics - Quantum Algebra 
@article{9807019,
     author = {Van der Jeugt, J. and Jagannathan, R.},
     title = {Realizations of $su(1,1)$ and $U\_q(su(1,1))$ and generating functions
  for orthogonal polynomials},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9807019}
}

Van der Jeugt, J.; Jagannathan, R. Realizations of $su(1,1)$ and $U_q(su(1,1))$ and generating functions
  for orthogonal polynomials. arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9807019/