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Spectral theory of invariant operators, sharp inequalities, and representation theory

Branson, Thomas — 1997

Proceedings of the 16th Winter School "Geometry and Physics"

The paper represents the lectures given by the author at the 16th Winter School on Geometry and Physics, Srni, Czech Republic, January 13-20, 1996. He develops in an elegant manner the theory of conformal covariants and the theory of functional determinant which is canonically associated to an elliptic operator on a compact pseudo-Riemannian manifold. The presentation is excellently realized with a lot of details, examples and open problems.

Spectrum generating on twistor bundle

Thomas Branson;  Doojin Hong — 2006

Archivum Mathematicum

Spectrum generating technique introduced by Ólafsson, Ørsted, and one of the authors in the paper (Branson, T., Ólafsson, G. and Ørsted, B., Spectrum generating operators, and intertwining operators for representations induced from a maximal parabolic subgroups, J. Funct. Anal. 135 (1996), 163–205.) provides an efficient way to construct certain intertwinors when K -types are of multiplicity at most one. Intertwinors on the twistor bundle over S 1 × S n - 1 have some K -types of multiplicity 2. With some additional...

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