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 -torsions for locally symmetric spaces.
On donne une formule géométrique explicite pour les intégrales orbitales semisimples tordues du noyau de la chaleur sur un espace symétrique, en utilisant la méthode du laplacien hypoelliptique développée par Bismut. Alors en combinant avec la formule des traces tordue, on peut évaluer les traces équivariantes de l’opérateur de la chaleur du laplacien sur un espace localement symétrique compact. En particulier, on revisite les théorèmes de l’indice équivariant local et de la torsion équivariante pour les espaces localement symétriques.
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Keywords: Twisted orbital integral, Casimir operator, Hypoelliptic Laplacian, Symmetric space
Mots-clés : Intégrale orbitale tordue, Opérateur de Casimir, Laplacien hypoelliptique, Espace symétrique
Liu, Bingxiao 1

@article{AIF_2023__73_5_1909_0, author = {Liu, Bingxiao}, title = {Hypoelliptic {Laplacian} and twisted trace formula}, journal = {Annales de l'Institut Fourier}, pages = {1909--1985}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {73}, number = {5}, year = {2023}, doi = {10.5802/aif.3566}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3566/} }
TY - JOUR AU - Liu, Bingxiao TI - Hypoelliptic Laplacian and twisted trace formula JO - Annales de l'Institut Fourier PY - 2023 SP - 1909 EP - 1985 VL - 73 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3566/ DO - 10.5802/aif.3566 LA - en ID - AIF_2023__73_5_1909_0 ER -
%0 Journal Article %A Liu, Bingxiao %T Hypoelliptic Laplacian and twisted trace formula %J Annales de l'Institut Fourier %D 2023 %P 1909-1985 %V 73 %N 5 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3566/ %R 10.5802/aif.3566 %G en %F AIF_2023__73_5_1909_0
Liu, Bingxiao. Hypoelliptic Laplacian and twisted trace formula. Annales de l'Institut Fourier, Volume 73 (2023) no. 5, pp. 1909-1985. doi : 10.5802/aif.3566. https://aif.centre-mersenne.org/articles/10.5802/aif.3566/
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