A graphical formalism is introduced for describing subgroup type coordinates on -dimensional Lorentzian hyperboloids imbedded into dimensional Minkowski spaces. The group element is parametrized according to different subgroup chains, involving Lorentz, rotation, and Euclidean subgroups. The coordinates are then induced by the corresponding group action. Eigenfunctions of the Laplace–Beltrami operator are obtained as products of Jacobi functions, associated Legendre functions, and modified Bessel functions.
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