A classification of coherent state representations of unimodular Lie groups
Wojciech Lisiecki
Source: Bull. Amer. Math. Soc. (N.S.) Volume 25, Number 1
(1991), 37-43.
First Page:
Show
Hide
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.bams/1183657043
Mathematical Reviews number (MathSciNet): MR1080614
Zentralblatt MATH identifier: 0736.22008
References
[AM] R. Abraham and J. Marsden, Foundations of mechanics, 2nd ed., Benjamin/Cummings, Reading, MA, 1978.
Zentralblatt MATH: 0393.70001
Mathematical Reviews (MathSciNet): MR515141
[Bl] F. A. Berezin, Quantization, Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), 1116-1175; English transl., in Math. USSR Izv. 38 (1974).
Zentralblatt MATH: 0312.53049
Mathematical Reviews (MathSciNet): MR395610
[B2] F. A. Berezin, Quantization in complex symmetric spaces, Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975), 363-402; English transl. in Math. USSR Izv. 39 (1975).
Zentralblatt MATH: 0312.53050
Mathematical Reviews (MathSciNet): MR508179
[DN] J. Dorfmeister and K. Nakajima, The fundamental conjecture for homogeneous Kaehler manifolds, Acta Math. 161 (1988), 23-70.
Zentralblatt MATH: 0662.32025
Mathematical Reviews (MathSciNet): MR962095
Digital Object Identifier: doi:10.1007/BF02392294
[EHW] T. Enright, R. Howe and N. Wallach, A classification of unitary highest weight modules, Representation Theory of Reductive Groups (P. Trombi, ed.), Progress in Math., vol. 40, Birkhäuser, Boston, 1983, pp. 97-143.
Zentralblatt MATH: 0535.22012
Mathematical Reviews (MathSciNet): MR733809
Digital Object Identifier: doi:10.1007/978-1-4684-6730-7_7
[Ha] J. I. Hano, On Kaehlerian homogeneous spaces of unimodular Lie groups, Amer. J. Math. 79 (1957), 885-900.
Zentralblatt MATH: 0096.16203
Mathematical Reviews (MathSciNet): MR95979
Digital Object Identifier: doi:10.2307/2372440
[Ho] R. Howe, θ-series and invariant theory, Automorphic Forms, Representations and L-functions, Proc. Sympos. Pure Math., vol. 33, Amer. Math. Soc., Providence, RI, 1979, pp. 275-285.
Zentralblatt MATH: 0423.22016
Mathematical Reviews (MathSciNet): MR546602
[J] H. P. Jakobsen, Hermitian symmetric spaces and their unitary highest weight modules, J. Funct. Anal. 52 (1983), 385-412.
Zentralblatt MATH: 0517.22014
Mathematical Reviews (MathSciNet): MR712588
Digital Object Identifier: doi:10.1016/0022-1236(83)90076-9
[K] S. Kobayashi, Irreducibility of certain unitary representations, J. Math. Soc. Japan 20 (1968), 638-642.
Zentralblatt MATH: 0165.40504
Mathematical Reviews (MathSciNet): MR231413
Digital Object Identifier: doi:10.2969/jmsj/02040638
Project Euclid: euclid.jmsj/1259943865
[KS] B. Kostant and S. Sternberg, Symplectic projective orbits, New Directions in Applied Mathematics, Springer-Verlag, Berlin and New York, 1982, pp. 81-84.
Zentralblatt MATH: 0484.22022
Mathematical Reviews (MathSciNet): MR661285
Digital Object Identifier: doi:10.1007/978-1-4612-5651-9_5
[L] W. Lisiecki, Kaehler coherent state orbits for representations of semisimple Lie groups, Ann. Inst. H. Poincaré Phys. Théor. 53 (1990), 245-258.
Zentralblatt MATH: 0724.22013
Mathematical Reviews (MathSciNet): MR1079780
[O1] A. Odzijewicz, On reproducing kernels and quantization of states, Comm. Math. Phys. 114 (1988), 577-597.
Zentralblatt MATH: 0645.53044
Mathematical Reviews (MathSciNet): MR929131
Digital Object Identifier: doi:10.1007/BF01229456
Project Euclid: euclid.cmp/1104160780
[O2] A. Odzijewicz, On the notion of mechanical system (to appear).
[P] A. M. Perelomov, Generalized coherent states and their applications, Springer-Verlag, Berlin and New York, 1986.
Zentralblatt MATH: 0605.22013
Mathematical Reviews (MathSciNet): MR858831
[S1] I. Satake, Unitary representations of a semi-direct product of Lie groups on $\bar \partial$-cohomology spaces, Math. Ann. 190 (1971), 177-202.
Zentralblatt MATH: 0205.04405
Mathematical Reviews (MathSciNet): MR296213
Digital Object Identifier: doi:10.1007/BF01433209
[S2] I. Satake, Algebraic structures of symmetric domains, Princeton Univ. Press, Princeton, NJ, 1980.
Zentralblatt MATH: 0483.32017
Mathematical Reviews (MathSciNet): MR591460
[T] G. M. Tuynman, Studies in geometric quantization, Ph.D. thesis, Amsterdam, 1987.
Mathematical Reviews (MathSciNet): MR827498
Zentralblatt MATH: 0584.58018
Bulletin (New Series) of the American Mathematical Society