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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 algebra arbitrary automorphism Cartan subgroup character commutative compact subgroup complementary series complex numbers complex semisimple group consider converges corresponding cosets decomposed decomposition defined denote diagonal direct sum Dokl eigenvalues equal equation equivalent finite finite-dimensional form g formula function ºf functions f(z Gelfand given group G Hence Hermitian homogeneous space horosphere horosphere space integral invariant measure irreducible representations irreducible unitary representations isomorphic kernel Lemma linear Lorentz group manifold mapping matrices of order matrix g multiplication Nauk SSSR non-degenerate norm numbers obtained operator pairs parameters permutation positive definite function principal series proved real numbers regular representation right cosets ring satisfying the condition semisimple group semisimple Lie group ſº space $5 space H space of functions spherical functions subgroup of G subspace symmetric space Theorem tion transformation two-sided cosets unimodular group uniquely variables vector zero