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• W220552908 abstract "This chapter describes the geometric constructions of representations. There is a close connection between representations of a Lie group G and its coadjoint orbits, that is, G -orbits in the dual of the Lie algebra. In the case of a nilpotent group, unitary representations correspond to coadjoint orbits equipped with real polarizations, and the correspondence has been used by Kirillov to construct the representations. Harish-Chandra's parametrization of those unitary representations that enter the Plancherel decomposition of L 2 (G) , with G semisimple, are phrased in terms of coadjoint orbits, though his construction ties the representations only indirectly to the orbits in question. The chapter describes recent results on the orbit method for semisimple coadjoint orbits of semisimple Lie groups, without restriction on the type of polarization." @default.
• W220552908 created "2016-06-24" @default.
• W220552908 creator A5080844938 @default.
• W220552908 date "1988-01-01" @default.
• W220552908 modified "2023-09-25" @default.
• W220552908 title "Geometric Constructions of Representations" @default.
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• W220552908 doi "https://doi.org/10.1016/b978-0-12-525100-6.50015-1" @default.
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