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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



A classification of coherent state representations of unimodular Lie groups

Author: Wojciech Lisiecki
Journal: Bull. Amer. Math. Soc. 25 (1991), 37-43
MSC (1985): Primary 22E45, 81D30; Secondary 32M10, 58F05, 58F06
MathSciNet review: 1080614
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  • [AM] R. Abraham and J. Marsden, Foundations of mechanics, 2nd ed., Benjamin/Cummings, Reading, MA, 1978. MR 515141
  • [Bl] F. A. Berezin, Quantization, Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), 1116-1175; English transl., in Math. USSR Izv. 38 (1974). MR 395610
  • [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). MR 508179
  • [DN] J. Dorfmeister and K. Nakajima, The fundamental conjecture for homogeneous Kaehler manifolds, Acta Math. 161 (1988), 23-70. MR 962095
  • [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. MR 733809
  • [Ha] J. I. Hano, On Kaehlerian homogeneous spaces of unimodular Lie groups, Amer. J. Math. 79 (1957), 885-900. MR 95979
  • [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. MR 546602
  • [J] H. P. Jakobsen, Hermitian symmetric spaces and their unitary highest weight modules, J. Funct. Anal. 52 (1983), 385-412. MR 712588
  • [K] S. Kobayashi, Irreducibility of certain unitary representations, J. Math. Soc. Japan 20 (1968), 638-642. MR 231413
  • [KS] B. Kostant and S. Sternberg, Symplectic projective orbits, New Directions in Applied Mathematics, Springer-Verlag, Berlin and New York, 1982, pp. 81-84. MR 661285
  • [L] W. Lisiecki, Kaehler coherent state orbits for representations of semisimple Lie groups, Ann. Inst. H. Poincaré Phys. Théor. 53 (1990), 245-258. MR 1079780
  • [O1] A. Odzijewicz, On reproducing kernels and quantization of states, Comm. Math. Phys. 114 (1988), 577-597. MR 929131
  • [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. MR 858831
  • [S1] I. Satake, Unitary representations of a semi-direct product of Lie groups on $\bar \partial$-cohomology spaces, Math. Ann. 190 (1971), 177-202. MR 296213
  • [S2] I. Satake, Algebraic structures of symmetric domains, Princeton Univ. Press, Princeton, NJ, 1980. MR 591460
  • [T] G. M. Tuynman, Studies in geometric quantization, Ph.D. thesis, Amsterdam, 1987. MR 827498

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