Laguerre Functions on Symmetric Cones and recursion relations in the Real Case
Classical Analysis and ODEs
2007-05-23 v1 Representation Theory
Abstract
In this article we derive differential recursion relations for the Laguerre functions on the cone C 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 C+ i Sym(n,R). We then use the Laplace transform to carry the Lie algebra action over to L^2(C ,dm_t). The differential recursion relations result by restricting to a distinguished three dimensional subalgebra, which is isomorphic to sl(2,R).
Keywords
Cite
@article{arxiv.math/0412199,
title = {Laguerre Functions on Symmetric Cones and recursion relations in the Real Case},
author = {Michael Aristidou and Mark Davidson and Gestur 'Olafsson},
journal= {arXiv preprint arXiv:math/0412199},
year = {2007}
}