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adjoint assume automorphism bounded Cartan subalgebra Cartan subgroup character choose commutes compact conjugate constant contains corollary corresponding decomposition defined over F denote differential operator discrete series Eisenstein integral element equal exact sequence exists finite finite-dimensional fixed point formula G-invariant Gc/B Harish-Chandra harmonic analysis Hence Hermitian metric Hilbert space holomorphic homogeneous induced infinitesimally equivalent inner product invariant irreducible representation isomorphism Langlands Lemma Levi factor Lie algebra line bundle linear functional linear transformation Math module nonzero orthogonal orthonormal parabolic subgroup polynomials positive roots principal series representations proof of Lemma Proposition prove psgp of G quasi-simple quasi-split representation of G respectively restriction satisfies scalar Schwartz space semisimple Lie group square-integrable subgroup of G subspace Suppose surjective Theorem topology trace class unique unitary representation vanishes vector bundle vector space Weyl chamber Weyl group zero
Transactions of the American Mathematical Society
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