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An application of shift operators to ordered symmetric spaces

Nils Byrial Andersen;  Jérémie M. Unterberger — 2002

Annales de l’institut Fourier

We study the action of elementary shift operators on spherical functions on ordered symmetric spaces ℳ m , n of Cayley type, where m ∈ ℕ denotes the multiplicity of the short roots and n ∈ ℕ the rank of the symmetric space. For m even we apply this to prove a Paley-Wiener theorem for the spherical Laplace transform defined on ℳ m , n by a reduction to the rank 1 case. Finally we generalize our notions and results to B C n type root systems.

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