Spherical functions on the de Sitter group

Details Spherical functions on the de Sitter group Spherical functions on the de Sitter group

2006-04-13

arxiv.org/abs/math-ph/0604026v2

J.Phys. A40 (2007) 163

Physics

Mathematical Physics

40 pages

Scientific paper

10.1088/1751-8113/40/1/010

Matrix elements and spherical functions of irreducible representations of the de Sitter group are studied on the various homogeneous spaces of this group. It is shown that a universal covering of the de Sitter group gives rise to quaternion Euler angles. An explicit form of Casimir and Laplace-Beltrami operators on the homogeneous spaces is given. Different expressions of the matrix elements and spherical functions are given in terms of multiple hypergeometric functions both for finite-dimensional and unitary representations of the principal series of the de Sitter group.

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