Group theory/Geometry
The multiplicities of the equivariant index of twisted Dirac operators
[Multiplicités de l'indice équivariant de l'opérateur de Dirac twisté]
Comptes Rendus. Mathématique, Tome 352 (2014) no. 9, pp. 673-677.

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.

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

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.05.001
@article{CRMATH_2014__352_9_673_0,
     author = {Paradan, Paul-\'Emile and Vergne, Mich\`ele},
     title = {The multiplicities of the equivariant index of twisted {Dirac} operators},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {673--677},
     publisher = {Elsevier},
     volume = {352},
     number = {9},
     year = {2014},
     doi = {10.1016/j.crma.2014.05.001},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2014.05.001/}
}
TY  - JOUR
AU  - Paradan, Paul-Émile
AU  - Vergne, Michèle
TI  - The multiplicities of the equivariant index of twisted Dirac operators
JO  - Comptes Rendus. Mathématique
PY  - 2014
SP  - 673
EP  - 677
VL  - 352
IS  - 9
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2014.05.001/
DO  - 10.1016/j.crma.2014.05.001
LA  - en
ID  - CRMATH_2014__352_9_673_0
ER  - 
%0 Journal Article
%A Paradan, Paul-Émile
%A Vergne, Michèle
%T The multiplicities of the equivariant index of twisted Dirac operators
%J Comptes Rendus. Mathématique
%D 2014
%P 673-677
%V 352
%N 9
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2014.05.001/
%R 10.1016/j.crma.2014.05.001
%G en
%F CRMATH_2014__352_9_673_0
Paradan, Paul-Émile; Vergne, Michèle. The multiplicities of the equivariant index of twisted Dirac operators. Comptes Rendus. Mathématique, Tome 352 (2014) no. 9, pp. 673-677. doi : 10.1016/j.crma.2014.05.001. http://www.numdam.org/articles/10.1016/j.crma.2014.05.001/

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

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

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

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

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

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

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

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

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

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

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

Cité par Sources :