A computation of the equivariant index of the Dirac operator

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1. [1] ALVAREZ-GAUMÉ (L.), Supersymmetry and the Atiyah-Singer Index theorem, Commun. Math. Phys. Vol. 90, No. 101, 1983, pp. 161-173. Zbl0528.58034MR85d:58078
2. [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. Zbl0578.58039MR87h:58206
3. [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. Zbl0161.43201MR35 #3701
4. [4] ATIYAH (M.F.) and SEGAL (G.B.), The index of elliptic operators II, Ann. of Math., Vol. 87, 1968, pp. 531-545. Zbl0164.24201MR38 #5244
5. [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. Zbl0164.24301
6. [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. Zbl0223.53034
7. [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. Zbl0604.58046MR87a:58143
8. [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. Zbl0521.57020MR83m:58002
9. [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. Zbl0556.58027
10. [10] DONNELLY (H.) and PATODI (V.K.), Spectrum and the fixed point set of Isometries II, Topology, Vol. 16, 1977, pp. 1-11. Zbl0341.53023MR55 #6489
11. [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. MR89b:58198
12. [12] GETZLER (E.), Pseudo differential operators on super manifolds and the Atiyah-Singer index theorem, Commun. Math. Phys., Vol. 92, 1983, pp. 163-178. Zbl0543.58026MR86a:58104
13. [13] GETZLER (E.), A short proof of the Atiyah-Singer Index Theorem (To appear). Zbl0607.58040
14. [14] GILKEY (P.), Curvature and eigenvalues of the Laplacian for elliptic complexes. Advances in Math., Vol. 10, 1973, pp. 344-382. Zbl0259.58010MR48 #3081
15. [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. Zbl0405.58044
16. [16] KIRILLOV (A.A.), Characters of unitary representations of Lie groups, Funct. Anal. App., Vol. 2-2, 1967, pp. 40-55. Zbl0174.45001MR38 #4615
17. [17] LICHNEROWICZ (A.), Spineurs Harmoniques, C.R. Acad. Sc., Vol. 257, 1963, pp. 7-9. Zbl0136.18401MR27 #6218
18. [18] MCKEAN (H.P.), SINGER (I.M.), Curvature and the eigenvalues of the Laplacian, J. Differential Geometry, Vol. 1, 1967, pp. 43-69. Zbl0198.44301MR36 #828
19. [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. Zbl0041.42701MR11,108b
20. [20] PATODI (V.K.), Curvature and the Eigenforms of the Laplace Operators, J. Diff. Geometry, Vol. 5, 1971, pp. 233-249. Zbl0211.53901MR45 #1201
21. [21] PATODI (V.K.), Analytic proof of the Riemann-Roch theorem for Kaehler manifolds, J. Diff. Geometry, Vol. 5, 1971, pp. 251-283. Zbl0219.53054MR44 #7502
22. [22] VERGNE (M.), Formule de Kirillov et indice de l'opérateur de Dirac, Proceedings of the International Congress of Mathematicians, 1983, Warszawa. Zbl0597.58033

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