Abstract:
In this paper we discuss the relation between representations of Lie groups and geometric quantizations. A series of representations of Lie groups are constructed by geometric quantization of coadjoint orbits. Particularly, all representations of compact Lie groups, holomorphic discrete series of representations and spherical representations of reductive Lie groups are constructed by geometric quantizations of elliptic and hyperbolic coadjoint orbits.
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Received: 2 January 1997 / Accepted: 1 October 1997
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Zhao, Q. The Representations of Lie Groups and¶Geometric Quantizations . Comm Math Phys 194, 135–148 (1998). https://doi.org/10.1007/s002200050352
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DOI: https://doi.org/10.1007/s002200050352