Inspired by the general theory of Kobayashi on the restriction of unitary representations of reductive groups such as Kobayashi’s multiplicity-one theorem and Kobayashi’s discretely decomposability theorem, we discuss their “classical limits” that are formulated in terms of the geometry of coadjoint orbits in certain special settings, according to the orbit philosophy by Krillov. The geometric quantizations in this chapter include non-tempered unitary representations corresponding to singular elliptic coadjoint orbits.

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Kobayashi’s Multiplicity-One Theorems in Branching Laws and Orbit Philosophy Beyond Tempered Representations

  • Salma Nasrin

摘要

Inspired by the general theory of Kobayashi on the restriction of unitary representations of reductive groups such as Kobayashi’s multiplicity-one theorem and Kobayashi’s discretely decomposability theorem, we discuss their “classical limits” that are formulated in terms of the geometry of coadjoint orbits in certain special settings, according to the orbit philosophy by Krillov. The geometric quantizations in this chapter include non-tempered unitary representations corresponding to singular elliptic coadjoint orbits.