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arXiv · 2112.11509

Geometric invariance of the semi-classical calculus on nilpotent graded Lie groups

Clotilde Fermanian Kammerer·Veronique Fischer·Steven Flynn
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Abstract

In this paper, we consider the semi-classical setting constructed on nilpotent graded Lie groups by means of representation theory. We analyze the effects of the pull-back by diffeomorphisms on pseudodifferential operators. We restrict to diffeomorphisms that preserve the filtration and prove that they are Pansu differentiable. We show that the pull-back of a semi-classical pseudodifferential operator by such a diffeomorphism has a semi-classical symbol that is expressed at leading order in terms of the Pansu differential. We interpret the geometric meaning of this invariance in the setting of filtered manifolds.

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Clotilde Fermanian Kammerer, Veronique Fischer, Steven Flynn. 2021-12-21. Geometric invariance of the semi-classical calculus on nilpotent graded Lie groups. https://doi.org/10.1007/s12220-022-01163-z

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