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1970a Some applications of the Schwartz space of a semisimple Lie group
1970c Harmonic analysis on semisimple Lie groups
1970d Harmonic analysis on reductive padic groups Introduction
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0-stable Cartan admissible representation assume automorphism bijection Cartan subalgebra Cartan subgroup character choose conclude from Lemma conj conjugate corollary of Lemma corresponding cusp forms cuspidal define denote the restriction denote the set denote the space differential operators discrete series distribution on G easy to verify Eisenstein integral Eisenstein Series element finite subset following property following result follows from Lemma function on G G-orbit Haar measure Harish-Chandra Harmonic analysis Hilbert space holomorphic irreducible Langlands decomposition Lemma Let f Let G Lie algebra Math meromorphic function Moreover nilpotent normalized Haar measure open compact subgroup parabolic parabolic subgroup positive roots prk G proof of Theorem proves psgp of G rank G representation of G roots of g Schwartz space semisimple Lie groups split component subgroup of G subspace Suppose vector x e G zero