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Second Order Operators on a Compact Lie Group

Published online by Cambridge University Press:  20 November 2018

H. D. Fegan  and
B. Steer
H. D. Fegan
Affiliation:
Department of Mathematics, Lehigh University, Bethlehem, PA 18015 U.S.A. e-mail: [email protected]
B. Steer
Affiliation:
Mathematical Institute, 24-29 St. Giles, Oxford OXI 3LB U.K. e-mail: [email protected]
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Abstract

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We describe the structure of the space of second order elliptic differential operators on a homogenous bundle over a compact Lie group. Subject to a technical condition, these operators are homotopic to the Laplacian. The technical condition is further investigated, with examples given where it holds and others where it does not. Since many spectral invariants are also homotopy invariants, these results provide information about the invariants of these operators.

Keywords

58J7043A77
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 57 , Issue 1 , 01 February 2005 , pp. 99 - 113
Copyright
Copyright © Canadian Mathematical Society 2005

References

[1] Bourbaki, N., Groupes et algèbres de Lie. Hermann, Paris, 1968, Ch. 4–6 .Google Scholar
[2] Branson, Thomas P., Conformally covariant equations on differential forms. Comm. Partial Differential Equations 7 (1982), 393–431.Google Scholar
[3] Epstein, D. B. A., Natural tensors on Riemannian manifolds. J. Differential Geometry 10 (1975), 631–645.Google Scholar
[4] Fegan, H. D., Second order operators with non-zero Eta Invariant. Canad. Math. Bull. 35 (1992), 341–353.Google Scholar
[5] Fegan, H. D. and Steer, B., First order operators on a manifold with a group action. Canad. J. Math. 48 (1996), 758–776.Google Scholar
[6] Gilkey, Peter B., The Eta invariant of even order operators. In: Differential Geometry, (eds. Carreras, F. J., Gil-Medrano, O. and Naviera, A. M.) Lecture Notes in Mathematics, 1410, Springer-Verlag, Berlin, 1989.Google Scholar
[7] Stredder, Peter, Natural differential operators on Riemannian manifolds and representations of the orthogonal and special orthogonal groups. J. Differential Geometry 10 (1975), 647–660.Google Scholar