Document Type

Article

Publication Date

12-1-2003

Abstract

In our previous papers we studied Laguerre functions and polynomials on symmetric cones Ω= H/L. The Laguerre functions ℓnv, n ∈, form an orthogonal basis in L2(Ω, dμv)L and are related via the Laplace transform to an orthogonal set in the representation space of a highest weight representations (πv, Hv) of the automorphism group G corresponding to a tube domain T(Ω). In this article, we consider the case where Ω is the space of positive definite Hermitian matrices and G = SU(n, n). We describe the Lie algebraic realization of πv acting in L 2(Ω, dμv) and use that to determine explicit differential equations and recurrence relations for the Laguerre functions.

Publication Source (Journal or Book title)

Integral Transforms and Special Functions

First Page

469

Last Page

484

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