Laguerre functions and representations of su (1,1)

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    Summary: Spectral analysis of a certain doubly inifinite Jacobi operator leads to orthogonality relations for confluent hypergeometric functios, which are called Laguerre functions. This doubly infinite Jacobi operator corresponds to the action of a parabolic element of the Lie algebra su$(1,1).$ The Clebsch-Gordan coefficients for the tensor product representation of a positive and a negative discrete series representation of su$(1,1)$ are determined for the parabolic bases. They turn out to be multiples of Jacobi functions. From the interpretation of Laguerre polynomials and functions as overlap coefficients, we obtain a product formula for the Laguerre polynomials, given by an integral over Laguerre functions, Jacobi functions and continuous dual Hahn polynomials. [ Ryszard Szwarc (Wroclaw) ]
    Original languageUndefined/Unknown
    Pages (from-to)329-352
    Number of pages24
    JournalIndagationes Mathematicae
    Issue number3-4
    Publication statusPublished - 2003

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