Preview
Unable to display preview. Download preview PDF.
References
R. L. Anderson, J. Fischer, and R. Raczka, “Coupling problem for U(p, q) ladder representations.” Proc. Roy. Sco. A. 302, 491–500 (1968).
L. Auslander and B. Kostant, “Polarization and Unitary Representations of Solvable Lie Groups”, Invent. Math. 14 (1971), 155–254.
V. Bargmann, “Group representations on Hilbert spaces of analytic function. Analytic methods in mathematical physics. ” Gordon and Breach.
Corwin-Ne'eman-Sternberg, “Graded Lie Algebras in mathematics and physics. ” Reviews of Modern Physics l47 (1975), 573–604.
S. Gelbart, “Harmonics on Stiefel Manifolds and generalized Hankel transforms.” Bull. Amer. Math. Soc. 78 (1972), 451–455.
S. Gelbart, “Holomorphic Discrete Series for the Real Symplectic Group”, Inventiones Math. 19 (1973), 49–58.
K. Gross and R. Kunze, “Bessel functions and representation theory, II. Holomorphic discrete series and metaplectic representations. ” J. Functional Analysis 25 (1977), 1–49.
V. Guillemin and S. Sternberg, Geometric Asymptotics, AMS Pub. (1977).
R. Howe, “Remarks on Classical Invariant Theory”, to appear.
C. Itzykson, Remarks on boson commutation rules, Commun. Math. Phys. 4 (1967), 92–122.
M. Kashiwara and M. Vergne, “On the Segal-Shale-Weil Representations and Harmonic polynomials. ” Preprint.
D. Kazhdan, B. Kostant and S. Sternberg, “On Hamiltonian group actions, etc. ” to appear.
B. Kostant, Quantization and Unitary Representations, Lecture Notes in Math. 170, (1969), 87-208, Springer-Verlag.
B. Kostant, “Graded manifolds, etc. ” in Differential geometric methods in mathematical physics, Springer Lecture Notes No. 570.
S. Kobayashi, Irreducibility of certain unitary representations, J. Math. Soc. Japan 20 (1968), 638–642.
G. Mack and I. Todorov “Irreducibility of the Ladder Representations of U(2,2) when Restricted to the Poincaré Subgroup.” J. Mathematical Phys. 10, 2078–2085
J. Marsden and A. Weinstein, “Reduction of Symplectic Manifolds with Symmetry”, Reports on Math. Phys. 5 (1974), 121–130.
G. W. Mackey, Unitary representations of group extensions, I, Acta Math. 99, (1958), 265–311.
D. Shale, Linear symmetries of free boson fields, Trans. Amer. Math. Soc. 103, (1962), 149–167.
D. Simms, Lectures on Geometric Quantization, Springer Lecture notes on Physics.
J. Sniatycki, “Geometric Quantization and Quantum mechanics.”
J. M. Souriau, Structure des Systemes Dynamiques, Dunod, Paris (1970).
J. M. Souriau, Construction explicite de l'indice de Maslov, etc., Nijmegen Conference, 1975.
S. Sternberg and J. Wolf, “Hermitian Lie Algebras and Metaplectic Representations”, to appear.
I. T. Todorov,Discrete Series of Hermitian Representations of the Lie Algebra of U(p, q). Lecture Notes.
N. Wallach, Analytic continuation of the discrete series, I and II, to appear.
A. Weil, “Sur certains groupes d'operateurs unitaries” Acta Math. 111 (1964), 193–211.
J. A. Wolf, “Unitary Representations of Maximal Parabolic Subgroups of the Classical Groups,” Memoirs Amer. Math. Soc. 180, 1976.
H. P. Jakobsen and M. Vergne, “Wave and Dirac operators and representations of the conformal group.” To appear.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1978 Springer-Verlag
About this paper
Cite this paper
Sternberg, S. (1978). Some recent results on the metaplectic representation. In: Kramer, P., Rieckers, A. (eds) Group Theoretical Methods in Physics. Lecture Notes in Physics, vol 79. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08848-2_7
Download citation
DOI: https://doi.org/10.1007/3-540-08848-2_7
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08848-6
Online ISBN: 978-3-540-35813-8
eBook Packages: Springer Book Archive