2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120272Matrix 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 pagesMathematical PhysicsGeneral Relativity and Quantum CosmologyHigh Energy Physics - Theory22E43; 22E70; 33C70; 35Q40text