@article{BSMF_1985__113__305_0,
author = {Berline, Nicole and Vergne, Mich\`ele},
title = {A computation of the equivariant index of the Dirac operator},
journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
volume = {113},
year = {1985},
pages = {305-345},
doi = {10.24033/bsmf.2036},
mrnumber = {87f:58146},
zbl = {0592.58044},
language = {en},
url = {http://dml.mathdoc.fr/item/BSMF_1985__113__305_0}
}
Berline, Nicole; Vergne, Michèle. A computation of the equivariant index of the Dirac operator. Bulletin de la Société Mathématique de France, Tome 113 (1985) pp. 305-345. doi : 10.24033/bsmf.2036. http://gdmltest.u-ga.fr/item/BSMF_1985__113__305_0/
[1] , Supersymmetry and the Atiyah-Singer Index theorem, Commun. Math. Phys. Vol. 90, No. 101, 1983, pp. 161-173. | MR 85d:58078 | Zbl 0528.58034
[2] , Circular symmetry and stationary phase approximation. In Proceedings of the Conference in honor of L. Schwartz, Asterisque, Paris, Vol. 131, 1985, pp. 43-60. | MR 87h:58206 | Zbl 0578.58039
[3] and , A Lefschetz fixed point formula for elliptic complexes, I. Ann. Math., Vol. 86, 1967, pp. 374-407 ; II, 88, 1968, pp. 451-481. | MR 35 #3701 | Zbl 0161.43201
[4] and , The index of elliptic operators II, Ann. of Math., Vol. 87, 1968, pp. 531-545. | MR 38 #5244 | Zbl 0164.24201
[5] and , The index of elliptic operators, I Ann. of Math., Vol. 87, 1968, pp. 484-530 ; III Ann. of Math., Vol. 87, 1968, pp. 546-604. | Zbl 0164.24301
[6] , and , Le spectre d'une variété riemannienne, Lecture notes in Mathematics, 194, Springer-Verlag, Berlin-Heidelberg-New York. | Zbl 0223.53034
[7] and , The equivariant index and Kirillov's character formula, Amer. Math. Soc, Amer. J. of Math., Vol. 107, n° 5, 1985, pp. 1159-1190. | MR 87a:58143 | Zbl 0604.58046
[8] and , Classes caractéristiques équivariantes. Formule de localisation en cohomologie équivariante, Comptes rendus Acad. Sc., Vol. 295, 1982, pp. 539-541. | MR 83m:58002 | Zbl 0521.57020
[9] , The Atiyah-Singer theorems. A Probabilistic approach. I The index theorem, J. Funct. Anal., Vol. 57, 1984, pp. 56-99. II The Lefschetz fixed point formulas, J. Funct. Anal., Vol. 57, 1984, pp. 329-348. | Zbl 0556.58027
[10] and , Spectrum and the fixed point set of Isometries II, Topology, Vol. 16, 1977, pp. 1-11. | MR 55 #6489 | Zbl 0341.53023
[11] and , Supersymmetric Derivation of the Atiyah-Singer Index and the Chiral Anomaly, Nuclear Physics B., Vol. B., No. 235 (FS 11), 1984, pp. 395-416. | MR 89b:58198
[12] , Pseudo differential operators on super manifolds and the Atiyah-Singer index theorem, Commun. Math. Phys., Vol. 92, 1983, pp. 163-178. | MR 86a:58104 | Zbl 0543.58026
[13] , A short proof of the Atiyah-Singer Index Theorem (To appear).
[14] , Curvature and eigenvalues of the Laplacian for elliptic complexes. Advances in Math., Vol. 10, 1973, pp. 344-382. | MR 48 #3081 | Zbl 0259.58010
[15] , Lefschetz fixed point formulas and the heat equation, in Partial Differential Equations and Geometry, Proceedings, Park-City Conference, 1977, Lecture Notes in Pure Appl. Math., No. 48, pp. 91-147, M. Dekker, New York, 1979. | Zbl 0405.58044
[16] , Characters of unitary representations of Lie groups, Funct. Anal. App., Vol. 2-2, 1967, pp. 40-55. | MR 38 #4615 | Zbl 0174.45001
[17] , Spineurs Harmoniques, C.R. Acad. Sc., Vol. 257, 1963, pp. 7-9. | MR 27 #6218 | Zbl 0136.18401
[18] , , Curvature and the eigenvalues of the Laplacian, J. Differential Geometry, Vol. 1, 1967, pp. 43-69. | MR 36 #828 | Zbl 0198.44301
[19] and , Some properties of the eigenfunctions of the Laplace operator on Riemannian manifolds, Canad. J. Math., Vol. 1, 1949, pp. 242-256. | MR 11,108b | Zbl 0041.42701
[20] , Curvature and the Eigenforms of the Laplace Operators, J. Diff. Geometry, Vol. 5, 1971, pp. 233-249. | MR 45 #1201 | Zbl 0211.53901
[21] , Analytic proof of the Riemann-Roch theorem for Kaehler manifolds, J. Diff. Geometry, Vol. 5, 1971, pp. 251-283. | MR 44 #7502 | Zbl 0219.53054
[22] , Formule de Kirillov et indice de l'opérateur de Dirac, Proceedings of the International Congress of Mathematicians, 1983, Warszawa. | Zbl 0597.58033