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.
@article{CRMATH_2014__352_9_673_0,
author = {Paul-\'Emile Paradan and Mich\`ele Vergne},
title = {The multiplicities of the equivariant index of twisted {Dirac} operators},
journal = {Comptes Rendus. Math\'ematique},
pages = {673--677},
year = {2014},
publisher = {Elsevier},
volume = {352},
number = {9},
doi = {10.1016/j.crma.2014.05.001},
language = {en},
}
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
[1] Quantization of presymplectic manifolds and circle actions, Trans. Amer. Math. Soc., Volume 352 (2000), pp. 525-552
[2] Construction de Représentations Unitaires d'un Groupe de Lie, CIME, Cortona, 1980
[3] Bott towers, complete integrability, and the extended character of representations, Duke Math. J., Volume 76 (1994), pp. 23-58
[4] Equivariant index and the moment map for completely integrable torus actions, Adv. Math., Volume 133 (1998), pp. 185-223
[5] Geometric quantization and multiplicities of group representations, Invent. Math., Volume 67 (1982), pp. 515-538
[6] The moment map and line bundles over presymplectic toric manifolds, J. Differ. Geom., Volume 38 (1993), pp. 465-484
[7] Symplectic surgery and the Spinc-Dirac operator, Adv. Math., Volume 134 (1998), pp. 240-277
[8] Singular reduction and quantization, Topology, Volume 38 (1999), pp. 699-763
[9] Localization of the Riemann–Roch character, J. Funct. Anal., Volume 187 (2001), pp. 442-509
[10] Spin-quantization commutes with reduction, J. Symplectic Geom., Volume 10 (2012), pp. 389-422
[11] An analytic proof of the geometric quantization conjecture of Guillemin–Sternberg, Invent. Math., Volume 132 (1998), pp. 229-259
Cited by Sources:
Comments - Policy
