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The Corwin-Greenleaf parity result fails for completely solvable Lie groups

1990
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Proceedings of the American Mathematical Society
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The results of Corwin-Greenleaf [1] on orbital decompositions of induced (and restricted) representations for simply connected nilpotent Lie groups have been extended to various kinds of Lie groups [2, 3]. In addition to explicit formulae for the spectrum and multiplicity, Corwin-Greenleaf were able to obtain some qualitative results on the multiplicity function in the direct integral. These results-in the nilpotent case of course-are: (1) the multiplicity is always uniformly infinite, or

doi:10.1090/s0002-9939-1990-1007506-9
fatcat:ruordbdcojhcvfqwugsbkffjjq