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Hypoelliptic Laplacian and Orbital Integrals (AM-177)
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Hypoelliptic Laplacian and Orbital Integrals (AM-177)

Jean-Michel Bismut


This book uses the hypoelliptic Laplacian to evaluate semisimple orbital integrals in a formalism that unifies index theory and the trace formula. The hypoelliptic Laplacian is a family of operators that is supposed to interpolate between the ordinary Laplacian and the geodesic flow. It is essentially the weighted sum of a harmonic oscillator along the fiber of the tangent bundle, and of the generator of the geodesic flow. In this book, semisimple orbital integrals associated with the heat kernel of the Casimir operator are shown to be invariant under a suitable hypoelliptic deformation, which ... More

Keywords: hypoelliptic Laplacian, orbital integrals, index theory, trace formula, geodesic flow, Casimir operator, hypoelliptic deformation, Kostant, wave kernel, Malliavin calculus

Bibliographic Information

Print publication date: 2011 Print ISBN-13: 9780691151298
Published to Princeton Scholarship Online: October 2017 DOI:10.23943/princeton/9780691151298.001.0001


Affiliations are at time of print publication.

Jean-Michel Bismut, author
Universite Paris Sud