A New Proof of Branson's Classification of Elliptic Generalized Gradients - Mathematics > Differential GeometryReport as inadecuate




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Abstract: We give a representation theoretical proof of Branson-s classification ofminimal elliptic sums of generalized gradients. The original proof uses toolsof harmonic analysis, which as powerful as they are, seem to be specific forthe structure groups SOn and Spinn. The different approach we propose isbased on the relationship between ellipticity and optimal Kato constants and onthe representation theory of son. Optimal Kato constants for ellipticoperators were computed by Calderbank, Gauduchon and Herzlich. We extend theirmethod to all generalized gradients not necessarily elliptic and recoverBranson-s result, up to one special case. The interest of this method is thatit is better suited to be applied for classifying elliptic sums of generalizedgradients of G-structures, for other subgroups G of the special orthogonalgroup.



Author: Mihaela Pilca

Source: https://arxiv.org/



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