Hypoelliptic Laplacian and twisted trace formula

Abstract

We give an explicit geometric formula for the twisted orbital integrals using the method of the hypoelliptic Laplacian developed by Bismut. Combining with the twisted trace formula, we can evaluate the equivariant trace of the heat operators of the Laplacians on a compact locally symmetric space. In particular, we revisit the equivariant local index theorems and twisted $L_2$-torsions for locally symmetric spaces.

60 pages. This article will appear at Annales de l'Institut Fourier. Note that this updated version contains only the first part of the previous version, while the second part has been revised as a separate article published in Journal of Functional Analysis with the title Asymptotic equivariant real analytic torsions for compact locally symmetric spaces

References in corpus (4)

• Exponential Estimate for the asymptotics of Bergman kernels
• Analytic torsion, dynamical zeta functions, and the Fried conjecture
• The twisted Selberg trace formula and the Selberg zeta function for compact orbifolds
• On the asymptotics of the analytic torsion for compact hyperbolic orbifolds