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Irreducible unitary representations of locally bicompact groups
Unitary representations of the group of linear transformations of
Spherical functions on symmetric Riemannian spaces
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affine space Akad arbitrary Cartan coincides commutative compact subgroup complex numbers consider constructed Corollary corresponding cosets decomposed decomposition defined denote diagonal Diff differential operator dimension direct sum Dokl eigenvalues elements equal equation equivalent exists finite finite-dimensional representations follows formula functor Gaussian measure Gelfand given graph group G Harish-Chandra Hence highest weight Hilbert space homogeneous space horosphere indecomposable integral invariant measure irreducible representations irreducible unitary representations isomorphism kernel Lemma Let G Lie algebra linear Lorentz group manifold mapping Math module monomial multiplication Nauk SSSR norm obtain orthogonal pair parameters permutation polynomial principal series proof Proposition prove quasi-invariant quasi-invariant measure relation representation of G respect ring roots satisfying the condition scalar product semisimple Lie group sequence space H space of functions spherical functions subset subspace tensor product Theorem tion transformation uniquely unitary representation variables vector Weyl Weyl group zero