Open AccessMinimal representations, geometric quantization, and unitarity.
Author(s) -
Ranee Brylinski,
Bertram Kostant
Publication year - 1994
Publication title -
proceedings of the national academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.91.13.6026
Subject(s) - symplectic geometry , mathematics , lie group , pure mathematics , nilpotent , unitary state , simple lie group , algebraic number , representation theory , geometric quantization , (g,k) module , algebra over a field , special unitary group , lie algebra , adjoint representation , simply connected space , fundamental representation , quantum , adjoint representation of a lie algebra , mathematical analysis , physics , lie conformal algebra , mathematical physics , quantum mechanics , weight , canonical quantization , political science , quantum gravity , law
In the framework of geometric quantization we explicitly construct, in a uniform fashion, a unitary minimal representation pio of every simply-connected real Lie group Go such that the maximal compact subgroup of Go has finite center and Go admits some minimal representation. We obtain algebraic and analytic results about pio. We give several results on the algebraic and symplectic geometry of the minimal nilpotent orbits and then "quantize" these results to obtain the corresponding representations. We assume (Lie Go)C is simple.
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