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Matrix Elements of the Irreducible Unitary Representations
The Reduction of the Product of Two Irreducible Unitary
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3.1 the domain According to Table BARGMANN boundary classes of irreducible Clebsch-Gordan coefficients complex valued functions corresponding coset spaces coshJ/2 decomposes decomposition defined direct integral direct sum discrete series dR(q dRp(q elements from 2.2.4 equivalence classes factor Fourier analysis function F given H^-basis Haar measure Hilbert space hypergeometric functions integral kernels integration path irreducible unitary representations isomorphic matrix elements momenta momentum multiplicities according negative real axis noncompact numbers obviously orthonormal basis parameter Plancherel plane Poincare group points principal and supplementary principal series product representation reduction problem repre representation space representation theory representations of H representations of SU(1,1 Representations of SU(2 respectively restricted representation restriction scalar product Sections 2.2 sentations single-valued spacelike square-integrable functions SU(1,1)-matrix elements SU(1,1)-representations SU(2)-matrix elements subgroup H subspaces substitution supplementary series symmetry relations tations tion unit circle unitarily unitary map unitary transformation yields z-plane zero