Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-08T12:25:24.006Z Has data issue: false hasContentIssue false
  • English
  • Français

Homogeneous Bundles and Universal Potentials

Published online by Cambridge University Press:  20 November 2018

H. D. Fegan
H. D. Fegan*
Affiliation:
Department of Mathematics and Statistics University of New Mexico Albuquerque, N.M. 87181
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper studies complex potentials on homogeneous bundles over a compact Lie group. It extends the previous work of V. Guillemin and A. Uribe on potentials isospectral to the zero potential. Then the notion of a universal potential is introduced, that is a potential which acts on sections by a group representation rather than as a scalar. Finally the inverse question of whether the spectral data of a complex potential on all bundles over S2 determines the potential is answered negatively.

Keywords

58G25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 4 , 01 December 1986 , pp. 398 - 406
Copyright
Copyright © Canadian Mathematical Society 1986

References

1. Eskin, G., Ralston, J., and Trubowitz, E., On Isospectral Periodic Potentials in ℝn , Comm. Pure and Applied Math., 37 (1984), pp. 647–676.Google Scholar
2. Fegan, H. D., The Spectrum of the Laplacian on Forms over a Lie group, Pacific J. Math., 90 (1980), pp. 373–387.Google Scholar
3. Guillemin, V. and Uribe, A., Spectral Properties of a Certain Class of Complex Potentials, Trans. Amer. Math. Soc, 279 (1983), pp. 759–771.Google Scholar
4. Helgason, S., Fundamental Solutions of Invariant Differential Operators on Symmetric Spaces, Amer. J. Math., 86 (1964), pp. 565–601.Google Scholar
5. Kostant, B., A Formula for the Multiplicity of a Weight, Trans. Amer. Math. Soc, 93 (1959), pp. 53–73.Google Scholar
6. McKean, H. and Van Moerbeke, P., The Spectrum of Hill s Equations, Invent. Math., 30 (1975), pp. 217–274.Google Scholar
7. Wallach, N. R., Harmonic Analysis on Homogeneous Spaces, M. Dekker, New York, 1973.Google Scholar