Differential Recursion Relations for Laguerre Functions on Hermitian Matrices
نویسنده
چکیده
Abstract. In our previous papers [1, 2] we studied Laguerre functions and polynomials on symmetric cones Ω = H/L. The Laguerre functions l n , n ∈ Λ, form an orthogonal basis in L(Ω, dμν ) and are related via the Laplace transform to an orthogonal set in the representation space of a highest weight representations (πν ,Hν) 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 πν acting in L(Ω, dμν) and use that to determine explicit differential equations and recurrence relations for the Laguerre functions.
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