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Correspondence between Lie algebra invariant subspaces and Lie group invariant subspaces of representations of Lie groups

1972
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Transactions of the American Mathematical Society
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Let G be a Lie group with Lie algebra 9 and 8 = u(g), the universal enveloping algebra of 9; also let U be a representation of G on H, a Hubert space, with dU the corresponding infinitesimal representation of 9 and S. For G semisimple Harish-Chandra has proved a theorem which gives a one-one correspondence between dU(o) invariant subspaces and U(G) invariant subspaces for certain representations U. This paper considers this theorem for more general Lie groups. A lemma is proved giving such a

doi:10.1090/s0002-9947-1972-0297928-x
fatcat:swr5zx5thfenxmluu6axplox6a