Abstract
The integral of a function over then'th power of hyperbolicd-dimensional spaceH is decomposed into integration along each orbit under diagonal action onH n of the isometry groupG onH, followed by integration over the orbit space, parametrized in terms of a complete set of invariants. The Jacobian entering in this last integral is expressed explicitly in terms of certain determinants. When viewingH as a half-hyperboloid in ℝ d+1 ,G is induced by the homogeneous Lorentz groupO ↑(1,d) acting on ℝ d+1 .
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Communicated by H. Araki
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Fuglede, B. Integration on then th power of a hyperbolic space in terms of invariants under diagonal action of isometries (Lorentz transformations). Commun.Math. Phys. 129, 481–509 (1990). https://doi.org/10.1007/BF02097102
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DOI: https://doi.org/10.1007/BF02097102