Remote Access Bulletin of the American Mathematical Society

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
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • Ralph Abraham and Jerrold E. Marsden, Foundations of mechanics, Benjamin/Cummings Publishing Co., Inc., Advanced Book Program, Reading, Mass., 1978. Second edition, revised and enlarged; With the assistance of Tudor Raţiu and Richard Cushman. MR 515141
  • F. A. Berezin, Quantization, Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), 1116–1175 (Russian). MR 0395610
  • F. A. Berezin, Quantization in complex symmetric spaces, Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975), no. 2, 363–402, 472 (Russian). MR 0508179
  • Josef Dorfmeister and Kazufumi Nakajima, The fundamental conjecture for homogeneous Kähler manifolds, Acta Math. 161 (1988), no. 1-2, 23–70. MR 962095, 10.1007/BF02392294
  • Thomas Enright, Roger Howe, and Nolan Wallach, A classification of unitary highest weight modules, Representation theory of reductive groups (Park City, Utah, 1982) Progr. Math., vol. 40, Birkhäuser Boston, Boston, MA, 1983, pp. 97–143. MR 733809
  • Jun-ichi Hano, On Kaehlerian homogeneous spaces of unimodular Lie groups, Amer. J. Math. 79 (1957), 885–900. MR 0095979
  • R. Howe, 𝜃-series and invariant theory, Automorphic forms, representations and 𝐿-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977) Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 275–285. MR 546602
  • Hans Plesner Jakobsen, Hermitian symmetric spaces and their unitary highest weight modules, J. Funct. Anal. 52 (1983), no. 3, 385–412. MR 712588, 10.1016/0022-1236(83)90076-9
  • Shoshichi Kobayashi, Irreducibility of certain unitary representations, J. Math. Soc. Japan 20 (1968), 638–642. MR 0231413
  • Bertram Kostant and Shlomo Sternberg, Symplectic projective orbits, New directions in applied mathematics (Cleveland, Ohio, 1980) Springer, New York-Berlin, 1982, pp. 81–84. MR 661285
  • W. Lisiecki, Kaehler coherent state orbits for representations of semisimple Lie groups, Ann. Inst. H. Poincaré Phys. Théor. 53 (1990), no. 2, 245–258 (English, with French summary). MR 1079780
  • Anatol Odzijewicz, On reproducing kernels and quantization of states, Comm. Math. Phys. 114 (1988), no. 4, 577–597. MR 929131
  • [O2] A. Odzijewicz, On the notion of mechanical system (to appear).
  • A. Perelomov, Generalized coherent states and their applications, Texts and Monographs in Physics, Springer-Verlag, Berlin, 1986. MR 858831
  • I. Satake, Unitary representations of a semi-direct product of Lie groups on ∂-cohomology spaces, Math. Ann. 190 (1970/71), 177–202. MR 0296213
  • Ichirô Satake, Algebraic structures of symmetric domains, Kanô Memorial Lectures, vol. 4, Iwanami Shoten, Tokyo; Princeton University Press, Princeton, N.J., 1980. MR 591460
  • G. M. Tuynman, Proceedings seminar 1983–1985: Mathematical structures in field theories. Vol. 1, CWI Syllabi, vol. 8, Stichting Mathematisch Centrum, Centrum voor Wiskunde en Informatica, Amsterdam, 1985. Geometric quantization. MR 827498

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1985): 22E45, 81D30, 32M10, 58F05, 58F06

Retrieve articles in all journals with MSC (1985): 22E45, 81D30, 32M10, 58F05, 58F06


Additional Information

DOI: https://doi.org/10.1090/S0273-0979-1991-16019-2