Holorphic morse inequalities in singular reduction

Mathematical Research Letters

Volumn 5, Issue 3, 1998, Pages 345-352

  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: 0032219328     PISSN: 10732780     EISSN: None     Source Type: Journal    
DOI: 10.4310/MRL.1998.v5.n3.a7     Document Type: Article

References (17)

1. [AS] M. F. Atiyah and I. M. Singer, The index of ellitptic operators, III, Ann. of Math. 87 (1968), 546-604.
2. [BL] J.-M. Bismut and G. Lebeau, Complex immersions and Quillen metrics, Publ. Math. IHES. 74 (1991), 1-297.
3. [DGMW] H. Duistermaart, V. Guillemin, E. Meinrenken, and S. Wu, Symplectic reduction and Riemann-Roch for circle actions, Math. Res. Lett. 2 (1995), 259-266.
4. [G] V. Guillemin, Reduced phase space and Riemann-Roch, Lie Groups and Geometry, R. Brylinski et al. ed., Birkhaeuser (Progress in Math., 123), 1995, pp. 305-334.
5. [GS] V. Guillemin and S. Sternberg, Geometric quantization and multiplicities of group representations, Invent. Math. 67 (1982), 515-538.
6. [JK] L. C. Jeffrey and F. C. Kirwan, Localization and quantization conjecture, Topology 36 (1997), 647-693.
7. [K1] F. C. Kirwan, Cohomology of quotients in symplectic and algebraic geometry, Princeton Univ. Press, Princeton, 1984.
8. [K2] -, Convexity properties of the moment mapping, III, Invent. Math. 77 (1984), 547-552.
9. [Ko] B. Kostant, Quantization and unitary representations, Modern Analysis and Applications, Lecture Notes in Math. vol. 170, Springer-Verlag, (1970), pp. 87-207.
10. [M1] E. Meinrenken, On Riemann-Roch formulas for multiplicities, J. Amer. Math. Soc. 9 (1996), 373-389.
11. c-Dirac operator, Adv. in Math. (to appear).
12. [MS] E. Meinrenken and R. Sjamaar, Singular reduction and quantization, Preprint, 1996 (dg-ga 9707023).
13. [McS] D. Mcduff and D. Salamon, Introduction to symplectic topology, Clarendon Press, Oxford, 1995.
14. [TZ1] Y. Tian and W. Zhang, Symplectic reduction and quantization, C. R. Acad. Sci. Paris, Série I 324 (1997), 433-438.
15. [TZ2] -, An analytic proof of the geometric quantization conjecture of Guillemin-Sternberg, Invent. Math. 132 (1998), 229-259.
16. [TZ3] -, Quantization formula for singular reductions, Preprint, 1997 (dg-ga 9706016).
17. [V] M. Vergne, Multiplicity formula for geometric quantization, I, II, Duke Math. J. 82 (1996), 143-179, 181-194.