Laguerre functions on symmetric cones and recursion relations in the real case
In this article we derive differential recursion relations for the Laguerre functions on the cone Ω of positive definite real matrices. The highest weight representations of the group Sp (n, R) play a fundamental role. Each such representation acts on a Hilbert space of holomorphic functions on the tube domain Ω + i Sym (n, R). We then use the Laplace transform to carry the Lie algebra action over to L2 (Ω, d μν). The differential recursion relations result by restricting to a distinguished three-dimensional subalgebra, which is isomorphic to sl (2, R) . © 2005 Elsevier B.V. All rights reserved.
Publication Source (Journal or Book title)
Journal of Computational and Applied Mathematics
Aristidou, M., Davidson, M., & Ólafsson, G. (2007). Laguerre functions on symmetric cones and recursion relations in the real case. Journal of Computational and Applied Mathematics, 199 (1), 95-112. https://doi.org/10.1016/j.cam.2005.12.002