Meixner functions and polynomials related to Lie algebra representations

Details Meixner functions and polynomials related to Lie algebra representations Meixner functions and polynomials related to Lie algebra representations

2001-09-25

arxiv.org/abs/math/0109201v1

J. Phys. A 35 (2002), no. 1, 65-85

Mathematics

Classical Analysis and ODEs

20 pages

Scientific paper

10.1088/0305-4470/35/1/306

The decomposition of the tensor product of a positive and a negative discrete series representation of the Lie algebra su(1,1) is a direct integral over the principal unitary series representations. In the decomposition discrete terms can occur, and the discrete terms are a finite number of discrete series representations or one complementary series representation. The interpretation of Meixner functions and polynomials as overlap coefficients in the four classes of representations and the Clebsch-Gordan decomposition, lead to a general bilinear generating function for the Meixner polynomials. Finally, realizing the positive and negative discrete series representations as operators on the spaces of holomorphic and anti-holomorphic functions respectively, a non-symmetric type Poisson kernel is found for the Meixner functions.

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