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Parabolic invariant theory and geometry. (English) Zbl 0798.53017
Eastwood, Michael (ed.) et al., The Penrose transform and analytic cohomology in representation theory. AMS-IMS-SIAM summer research conference, June 27 - July 3, 1992, South Hadley, MA, USA. Providence, RI: American Mathematical Society. Contemp. Math. 154, 169-180 (1993).
The paper is a report on [the author, M. G. Eastwood and C. R. Graham, Invariant theory for conformal and C-R geometry, to appear in Ann. Math.] It is well known that local invariants of Riemannian metrics are related to invariants of the orthogonal group. This has had important applications in the heat kernel proof of the Atiyah-Singer index formula. Similarly, local invariants of conformal structures and of C-R structures are related to invariants of modules for parabolic subgroups of semi- simple Lie groups. In the present paper the methods of the study of such invariants are demonstrated in one particular example.
For the entire collection see [Zbl 0780.00026].
Reviewer: C.Bär (Freiburg)
MSC:
53A55 Differential invariants (local theory), geometric objects
53A30 Conformal differential geometry (MSC2010)
32V99 CR manifolds
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