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Meixner functions and polynomials related to Lie algebra representations

Wolter Groenevelt·Erik Koelink
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Abstract

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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Wolter Groenevelt, Erik Koelink. 2001-09-25. Meixner functions and polynomials related to Lie algebra representations. https://doi.org/10.1088/0305-4470%2F35%2F1%2F306

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