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abelian admissible representation assume automorphism Cartan subgroup class function cohomology compact subgroup complex conjecture conjugate contains convex COROLLARY corresponding coset decomposition define denote differential operators direct sum discrete series characters discrete series representations distributions element equivalent finite dimensional follows Fourier transform Gelfand pair geodesic group G Haar measure Harish Harish-Chandra harmonic analysis Hecke algebra Hence Hermitian highest weight Hilbert space holomorphic discrete series homogeneous spaces homology induced infinitesimal character invariant involution irreducible admissible representation irreducible representation isomorphism Iwahori kernel Lemma Let G Lie algebra linear Math Mathematics matrix maximal module multiplicity noncompact notation orbital integrals orthogonal p-adic groups parabolic subalgebra parabolic subgroup Plancherel formula positive roots PROOF Proposition reductive groups representation of G representation theory representation TT restriction result semigroup semisimple Lie groups simple roots subgroup of G subset subspace supercuspidal representations Suppose symmetric spaces two-structure unipotent unitary representations vector Weyl group
References for Harish-Chandra
Harish-Chandra – Wikipedia