Abstract
The minimal dimensional co-adjoint orbits are determined for the real and complex classical Lie groups, and the representations associated to them by methods of geometric quantization are discussed. Some new computational methods are developed for the classical Lie algebras.
Keywords
- Unitary Representation
- Parabolic Subgroup
- Geometric Quantization
- Parabolic Subalgebra
- Principal Series Representation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Expanded version of part of a lecture at the conference "Differential Geometric Methods in Mathematical Physics," Bonn, July 13–16, 1977. Research partially supported by National Science Foundation Grant MPS-76-01692.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
K.I. Gross and R.A. Kunze, Bessel functions and representation theory, I, J. Functional Analysis 22 (1976), 73–105; II, ibid. 25 (1977), 1–49.
V. Guillemin and S. Sternberg, "Geometric Asymptotics," Math. Surveys No. 14, Amer. Math. Soc., Providence, 1977
R. Howe, Remarks on classical invariant theory, Yale University preprint, 1976.
D. Kazhdan, B. Kostant and S. Sternberg, Hamiltonian group actions and dynamical systems of Calagero type, Harvard University preprint, 1977.
E. Onofri, Dynamical Quantization of the Kepler Manifold, Università Parma (Inst. di Fisica) preprint, 1975.
J.H. Rawnsley, On the cohomology groups of a polarization and diagonal quantisation, Trans. Amer. Math. Soc. 230 (1977), 235–255.
W. Schmid, L 2-cohomology and the discrete series, Ann. of Math. 103 (1976), 375–394.
D.J. Simms, Metalinear structures and the quantization of the harmonic oscillator, Colloque Symplectique, Aix-en-Provence, 1974.
S. Sternberg, article in this volume.
S. Sternberg and J.A. Wolf, Hermitian Lie algebras and metaplectic representations, Trans. Amer. Math. Soc., to appear.
A. Weil, Sur certain groupes d'opérateurs unitaires, Acta Math. 111 (1964), 143–311.
J.A. Wolf, The action of a real semisimple Lie group on a complex flag manifold, II: Unitary representations on partially holomorphic cohomology spaces, Amer. Math. Soc, Memoir 138, 1974.
J.A. Wolf, Unitary representations of maximal parabolic subgroups of the classical groups, Amer. Math. Soc. Memoir 180, 1976.
J.A. Wolf, Conformal group, quantization, and the Kepler problem, in "Group Theoretical Methods in Physics," Fourth International Colloquium, Nijmegen 1975. Springer Lecture Notes in Physics 50 (1976), 217–222.
J.A. Wolf, Representations that remain irreducible on parabolic subgroups, to appear.
N. Woodhouse, Twistor theory and geometric quantization, in "Group Theoretical Methods in Physics," Fourth International Colloquium, Nijmegen 1975. Springer Lecture Notes in Physics 50 (1976), 149–163.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1978 Springer-Verlag
About this paper
Cite this paper
Wolf, J.A. (1978). Representations associated to minimal co-adjoint orrits. In: Bleuler, K., Reetz, A., Petry, H.R. (eds) Differential Geometrical Methods in Mathematical Physics II. Lecture Notes in Mathematics, vol 676. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0063679
Download citation
DOI: https://doi.org/10.1007/BFb0063679
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08935-3
Online ISBN: 978-3-540-35721-6
eBook Packages: Springer Book Archive
