Comptes Rendus
no. 9
Group theory/Geometry
The multiplicities of the equivariant index of twisted Dirac operators
[Multiplicités de l'indice équivariant de l'opérateur de Dirac twisté]

Présenté par : Michèle Vergne

Comptes Rendus. Mathématique, Volume 352 (2014) no. 9, pp. 673-677.

In this note, we give a geometric expression for the multiplicities of the equivariant index of a Dirac operator twisted by a line bundle.

Le but de cette note est de donner une expression géométrique pour les multiplicités de l'indice équivariant de l'opérateur de Dirac tordu par un fibré en lignes.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.05.001 
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Paul-Émile Paradan; Michèle Vergne. The multiplicities of the equivariant index of twisted Dirac operators. Comptes Rendus. Mathématique, Volume 352 (2014) no. 9, pp. 673-677. doi : 10.1016/j.crma.2014.05.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.05.001/

[1] A. Cannas da Silva; Y. Karshon; S. Tolman Quantization of presymplectic manifolds and circle actions, Trans. Amer. Math. Soc., Volume 352 (2000), pp. 525-552

[2] M. Duflo Construction de Représentations Unitaires d'un Groupe de Lie, CIME, Cortona, 1980

[3] M. Grossberg; Y. Karshon Bott towers, complete integrability, and the extended character of representations, Duke Math. J., Volume 76 (1994), pp. 23-58

[4] M. Grossberg; Y. Karshon Equivariant index and the moment map for completely integrable torus actions, Adv. Math., Volume 133 (1998), pp. 185-223

[5] V. Guillemin; S. Sternberg Geometric quantization and multiplicities of group representations, Invent. Math., Volume 67 (1982), pp. 515-538

[6] Y. Karshon; S. Tolman The moment map and line bundles over presymplectic toric manifolds, J. Differ. Geom., Volume 38 (1993), pp. 465-484

[7] E. Meinrenken Symplectic surgery and the Spinc-Dirac operator, Adv. Math., Volume 134 (1998), pp. 240-277

[8] E. Meinrenken; R. Sjamaar Singular reduction and quantization, Topology, Volume 38 (1999), pp. 699-763

[9] P.-E. Paradan Localization of the Riemann–Roch character, J. Funct. Anal., Volume 187 (2001), pp. 442-509

[10] P.-E. Paradan Spin-quantization commutes with reduction, J. Symplectic Geom., Volume 10 (2012), pp. 389-422

[11] Y. Tian; W. Zhang An analytic proof of the geometric quantization conjecture of Guillemin–Sternberg, Invent. Math., Volume 132 (1998), pp. 229-259

  • Peng Wang; Shuai Yin; Zhongmin Shen; Tong Zhu; Wenkai Zhang Geochemical Characteristics and Origin of Formation Water From the Upper Triassic Xujiahe Tight Sandstone in the Xiaoquan-Fenggu Structural Belt, Western Sichuan Depression, China, Frontiers in Earth Science, Volume 9 (2021) | DOI:10.3389/feart.2021.793170
  • Peter Hochs; Yanli Song; Shilin Yu A geometric realisation of tempered representations restricted to maximal compact subgroups, Mathematische Annalen, Volume 378 (2020) no. 1-2, pp. 97-152 | DOI:10.1007/s00208-020-02006-4 | Zbl:1454.22011
  • Peter Hochs; Yanli Song; Shilin Yu A geometric formula for multiplicities of K-types of tempered representations, Transactions of the American Mathematical Society, Volume 372 (2019) no. 12, pp. 8553-8586 | DOI:10.1090/tran/7857 | Zbl:1429.22015
  • Paul-Emile Paradan; Michèle Vergne Witten non abelian localization for equivariant K-theory, and the [Q,R]=0 theorem, Memoirs of the American Mathematical Society, 1257, Providence, RI: American Mathematical Society (AMS), 2019 | DOI:10.1090/memo/1257 | Zbl:1439.58015
  • P.-E. Paradan; M. Vergne Admissible coadjoint orbits for compact Lie groups, Transformation Groups, Volume 23 (2018) no. 3, pp. 875-892 | DOI:10.1007/s00031-017-9457-2 | Zbl:1404.22013
  • Peter Hochs; Yanli Song Equivariant indices of Spinc-Dirac operators for proper moment maps, Duke Mathematical Journal, Volume 166 (2017) no. 6, pp. 1125-1178 | DOI:10.1215/00127094-3792923 | Zbl:1370.58010
  • Peter Hochs; Yanli Song An equivariant index for proper actions. III: The invariant and discrete series indices, Differential Geometry and its Applications, Volume 49 (2016), pp. 1-22 | DOI:10.1016/j.difgeo.2016.07.003 | Zbl:1352.53042
  • Maxim Braverman The index theory on non-compact manifolds with proper group action, Journal of Geometry and Physics, Volume 98 (2015), pp. 275-284 | DOI:10.1016/j.geomphys.2015.08.014 | Zbl:1329.58021

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