Hypoelliptic Laplacian and twisted trace formula

Bingxiao Liu

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arXiv · 1910.11382

Hypoelliptic Laplacian and twisted trace formula

Bingxiao Liu

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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.

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Bingxiao Liu. 2019-10-24. Hypoelliptic Laplacian and twisted trace formula. https://arxiv.org/abs/1910.11382

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