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Solvable groups in general
34 other sections not shown
abelian admissible representation Amer American Mathematical Society analytic automorphism Borel boundary Cartan subgroup character compact subgroup compact support complex connected constant convergence Corollary corresponding decomposition defined Definition denote differential operator discrete series distribution dual elements equivalent exists finite Fourier transform functions on G G-space given group G Haar measure Harish-Chandra harmonic analysis Hence Hilbert space holomorphic implies induced representation integral invariant irreducible representations irreducible unitary isomorphism Kirillov Kostant Lemma Let G Lie algebra linear locally compact Math maximal Moreover nilpotent groups notation orbit p-adic parabolic subgroup Plancherel formula Plancherel measure polarization polynomial principal series problem proof Proposition prove representation of G restriction roots satisfies semisimple Lie groups solvable groups spherical functions square-integrable subalgebra subgroup of G subject classifications 1970 subset subspace supercuspidal symmetric spaces Theorem tion unipotent unique unitary representations vector space Weyl Weyl group