Analysis on flat symmetric spaces

Salem Ben Said (1) , Bent Orsted (2)

1 IECN - Institut Élie Cartan de Nancy
2 Aarhus University [Aarhus]

By taking an appropriate zero-curvature limit, we obtain the spherical functions on flat symmetric spaces G_o/K as limits of the Harish-Chandra's spherical functions. New and explicit formulas for the spherical functions on G_o/K are given. For symmetric spaces with root system of type A_n, we find the Taylor expansion of the spherical functions on G_o/K in a series of the Jack polynomials.

Domaines: Analyse fonctionnelle [math.FA]

Salem Ben Said, Bent Orsted. Analysis on flat symmetric spaces. Journal de Mathématiques Pures et Appliquées, 2005, 84, pp.1393--1426. ⟨hal-00095120⟩