A computation of the equivariant index of the Dirac operator
Bulletin de la Société Mathématique de France, Volume 113  (1985), p. 305-345
@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},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {113},
     year = {1985},
     pages = {305-345},
     doi = {10.24033/bsmf.2036},
     zbl = {0592.58044},
     mrnumber = {87f:58146},
     language = {en},
     url = {http://www.numdam.org/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, Volume 113 (1985) , pp. 305-345. doi : 10.24033/bsmf.2036. http://www.numdam.org/item/BSMF_1985__113__305_0/

[1] Alvarez-Gaumé (L.), 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] Atiyah (M.F.), 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] Atiyah (M.F.) and Bott (R.), 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] Atiyah (M.F.) and Segal (G.B.), The index of elliptic operators II, Ann. of Math., Vol. 87, 1968, pp. 531-545. | MR 38 #5244 | Zbl 0164.24201

[5] Atiyah (M.F.) and Singer (I.M.), 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] Berger (M.), Gauduchon (P.) and Mazet (E.), Le spectre d'une variété riemannienne, Lecture notes in Mathematics, 194, Springer-Verlag, Berlin-Heidelberg-New York. | Zbl 0223.53034

[7] Berline (N.) and Vergne (M.), 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] Berline (N.) and Vergne (M.), 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] Bismut (J.M.), 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] Donnelly (H.) and Patodi (V.K.), Spectrum and the fixed point set of Isometries II, Topology, Vol. 16, 1977, pp. 1-11. | MR 55 #6489 | Zbl 0341.53023

[11] Friedan (D.) and Windey (H.), 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] Getzler (E.), 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] Getzler (E.), A short proof of the Atiyah-Singer Index Theorem (To appear).

[14] Gilkey (P.), 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] Gilkey (P.), 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] Kirillov (A.A.), Characters of unitary representations of Lie groups, Funct. Anal. App., Vol. 2-2, 1967, pp. 40-55. | MR 38 #4615 | Zbl 0174.45001

[17] Lichnerowicz (A.), Spineurs Harmoniques, C.R. Acad. Sc., Vol. 257, 1963, pp. 7-9. | MR 27 #6218 | Zbl 0136.18401

[18] Mckean (H.P.), Singer (I.M.), Curvature and the eigenvalues of the Laplacian, J. Differential Geometry, Vol. 1, 1967, pp. 43-69. | MR 36 #828 | Zbl 0198.44301

[19] Minakshisundaram (S.) and Pleuel (A.), 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] Patodi (V.K.), Curvature and the Eigenforms of the Laplace Operators, J. Diff. Geometry, Vol. 5, 1971, pp. 233-249. | MR 45 #1201 | Zbl 0211.53901

[21] Patodi (V.K.), 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] Vergne (M.), Formule de Kirillov et indice de l'opérateur de Dirac, Proceedings of the International Congress of Mathematicians, 1983, Warszawa. | Zbl 0597.58033