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Laguerre Functions on Symmetric Cones and recursion relations in the Real Case

Michael Aristidou·Mark Davidson·Gestur 'Olafsson
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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).

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Michael Aristidou, Mark Davidson, Gestur 'Olafsson. 2004-12-09. Laguerre Functions on Symmetric Cones and recursion relations in the Real Case. https://arxiv.org/abs/math/0412199

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