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First Order Operators on Manifolds With a Group Action

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 18015-3174 U.S.A.
B. Steer
Affiliation:
Hertford College Oxford OX1 3BW U.K.
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Abstract

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We investigate questions of spectral symmetry for certain first order differential operators acting on sections of bundles over manifolds which have a group action. We show that if the manifold is in fact a group we have simple spectral symmetry for all homogeneous operators. Furthermore if the manifold is not necessarily a group but has a compact Lie group of rank 2 or greater acting on it by isometries with discrete isotropy groups, and let D be a split invariant elliptic first order differential operator, then D has equivariant spectral symmetry.

Keywords

58G3557S25
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 4 , 01 August 1996 , pp. 758 - 776
Copyright
Copyright © Canadian Mathematical Society 1996

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