Spherical functions on the de Sitter group
arXiv:math-ph/0604026 · doi:10.1088/1751-8113/40/1/010
Abstract
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.
40 pages
References in corpus (7)
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- Maxwell field on the Poincare group
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- General Solutions of Relativistic Wave Equations II: Arbitrary Spin Chains
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Cited by in corpus (6)
- Group Averaging for de Sitter free fields
- Spinor Structure and Internal Symmetries
- Group averaging for de Sitter free fields in terms of hyperspherical functions
- Eigenfunction Expansions of Functions Describing Systems with Symmetries
- Spinor Structure and Modulo 8 Periodicity
- Group Theoretical Description of Mendeleev Periodic System