no. 5
Hypoelliptic Laplacian and twisted trace formula
[Lapalcien hypoelliptique et formule des traces tordue]
Liu, Bingxiao1
1 Universität zu Köln Weyertal 86-90 D-50931 Köln (Deutschland)
Annales de l'Institut Fourier, Tome 73 (2023) no. 5, pp. 1909-1985.

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 L 2 équivariante pour les espaces localement symétriques.

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.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/aif.3566
Classification : 22E30, 53C35, 58J20, 58J50
Keywords: Twisted orbital integral, Casimir operator, Hypoelliptic Laplacian, Symmetric space
Mot clés : Intégrale orbitale tordue, Opérateur de Casimir, Laplacien hypoelliptique, Espace symétrique
Liu, Bingxiao 1

1 Universität zu Köln Weyertal 86-90 D-50931 Köln (Deutschland)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Liu, Bingxiao. Hypoelliptic Laplacian and twisted trace formula. Annales de l'Institut Fourier, Tome 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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