Journal of Lie Theory 19 (2009), No. 1, 149--183
Copyright Heldermann Verlag 2009
Families of Equivariant Differential Operators and Anti-de Sitter Spaces
Pierre Bäcklund
Mathematical Department, Uppsala University, Box 480, 751 06 Uppsala, Sweden
pierre@math.uu.se
We prove the existence and uniqueness of a sequence of differential intertwining operators for principal series representations, which are realized on boundaries of anti-de Sitter spaces. Algebraically, these operators correspond to homomorphisms of generalized Verma modules. We relate these families to the asymptotics of eigenfunctions on anti-de Sitter spaces.
Keywords: Anti-de Sitter space, spectral geometry, scattering theory, intertwining operators, Verma modules, conformal differential geometry.
MSC: 58J50; 22E30, 22E47, 43A85, 53A30
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