An analytic proof of the geometric quantization conjecture of Guillemin-Sternberg

Inventiones Mathematicae

Volumn 132, Issue 2, 1998, Pages 229-259

  Tian, Youliang ^a   Zhang, Weiping ^b  

^a NEW YORK UNIVERSITY   (United States)

^b NANKAI UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040427938     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002220050223     Document Type: Article

References (32)

1. M. F. Atiyah, I.M. Singer: The index of elliptic operators III. Ann. of Math. 87, 546-604 (1968)
2. N. Berline, E. Getzler, M. Vergne: Heat Kernels and Dirac Operators. Grundl. der Math. Wiss. vol. 298, Springer, 1992
3. J.-M. Bismut, G. Lebeau: Complex immersions and Quillen metrics. Publ. Math. IHES. 74, 1-297 (1991)
4. H. Duistermaat, V. Guillemin, E. Meinrenken, S. Wu: Symplectic reduction and Riemann-Roch for circle actions. Math. Res. Lett. 2, 259-266 (1995)
5. V. Guillemin: Reduced phase space and Riemann-Roch. in Lie Groups and Geometry, R. Brylinski et al. ed., Birkhäuser (Progress in Math., 123), 1995, pp. 305-334
6. P. Griffiths, J. Harris: Principles of Algebraic Geometry. John Wiley and Sons, 1978.
7. V. Guillemin, S. Sternberg: Geometric quantization and multiplicities of group representations. Invent. Math. 67, 515-538 (1982)
8. F. Hirzebruch: Elliptic genera of level N for complex manifolds, in Differential Geometric Methods in Theoretical Physics, Kluwer, Dordrecht, 1988, pp. 37-63
9. L. C. Jeffrey, F. C. Kirwan: Localization and quantization conjecture. Topology 36, 647-693 (1997)
10. L. C. Jeffrey, F. C. Kirwan: Localization for nonabelian group actions. Topology 34, 291-327 (1995)
11. F. C. Kirwan: Cohomology of Quotients in Symplectic and Algebraic Geometry. Princeton Univ. Press, Princeton, 1984
12. F. C. Kirwan: Convexity properties of the moment mapping, III. Invent. Math. 77, 547-552 (1984)
13. B. Kostant: Quantization and unitary representations, in Modern Analysis and Applications. Lecture Notes in Math. vol. 170, Springer-Verlag, (1970), pp. 87-207
14. H. B. Lawson, M.-L. Michelsohn: Spin Geometry. Princeton Univ. Press, 1989
15. E. Lerman: Symplectic cuts. Math. Res. Lett. 2, 247-258 (1995).
16. A. Lichnerowicz, Spineurs harmoniques. C. R. Acad. Sci. Paris, Série I, 257, 7-9 (1963)
17. K. Liu: Remarks on nonabelian localization. Intern. Math. Res. Notices No. 13, 683-691 (1995)
18. E. Meinrenken: On Riemann-Roch formulas for multiplicities. J. A. M. S. 9, 373-389 (1996)
19. c-Dirac operator. Adv. in Math. To appear
20. E. Meinrenken, R. Sjamaar: Singular reduction and quantization. Preprint, (dg-ga/ 9707023) 1996
21. V. Mathai, S. Wu: Equivariant holomorphic Morse inequalities I: a heat kernel proof. J. Diff. Geom. 46, 78-98 (1997)
22. D. Mcduff, D. Salamon: Introduction to Symplectic Topology. Clarendon Press, Oxford, 1995
23. R. Sjamaar: Symplectic reduction and Riemann-Roch formulas for multiplicities. Bull. A. M. S. 38, 327-338 (1996)
24. Y. Tian, W. Zhang: Symplectic reduction and quantization. C. R. Acad. Sci. Paris, Série I, 324, 433-438 (1997)
25. Y. Tian and W. Zhang: Symplectic reduction and analytic localization. Preprint, 1996
26. M. Vergne: Multiplicity formula for geometric quantization. Part I. Duke Math. J. 82, 143-179 (1996)
27. M. Vergne: Multiplicity formula for geometric quantization. Part II. Duke Math. J. 82, 181-194 (1996)
28. M. Vergne: A note on the Jeffrey-Kirwan-Witten localisation formula. Topology 35, 243-266 (1996)
29. E. Witten: Two dimensional gauge theories revisited. J. Geom. Phys. 9, 303-368 (1992)
30. E. Witten: Holomorphic Morse inequalities. in Algebraic and Differential Topology, Teubner-Texte Math. Vol. 70, Ed. G. Rassias, Teubner (Leipzig, 1984), pp. 318-333
31. S. Wu: An integration formula for the square of moment maps of circle actions. Lett. Math. Phys. 29, 311-328 (1993)
32. S. Wu, W. Zhang: Equivariant holomorphic Morse inequalities III: non-isolated fixed points. Preprint, 1997 (dg-ga/9701009), To appear in GAFA