Quantization Commutes with Reduction, a Survey

1. Atiyah M F. Elliptic Operators and Compact Groups. Lecture Notes in Mathematics, Vol 401. Berlin: Springer-Verlag, 1974

   Book  Google Scholar 

2. Berline N, Getzler E, Vergne M. Heat Kernels and Dirac Operators. Grundl Math Wiss Band 298. Berlin: Springer-Verlag, 1992

   Book  Google Scholar 

3. Bismut J-M, Lebeau G. Complex immersions and Quillen metrics. Inst Hautes Études Sci Publ Math, 1991, 74: 1–298

   Article  MathSciNet  Google Scholar 

4. Guillemin V, Sternberg S. Geometric quantization and multiplicities of group representations. Invent Math, 1982, 67(3): 515–538

   Article  MathSciNet  Google Scholar 

5. Hochs P, Mathai V. Geometric quantization and families of inner products. Adv Math, 2015, 282: 362–426

   Article  MathSciNet  Google Scholar 

6. Hochs P, Song Y. Equivariant indices of Spin-Dirac operators for proper moment maps. Duke Math J, 2017, 166: 1125–1178

   Article  MathSciNet  Google Scholar 

7. Hsiao C -Y, Ma X, Marinescu G. Geometric quantization on CR manifolds. arXiv:1906.05627

8. Kostant B. Quantization and unitary representations//Lect Notes in Math, 170. Springer, 1970: 87–207

9. Ma X. Geometric quantization on Kähler and symplectic manifolds//Proceedings of the International Congress of Mathematicians, Volume II (New Delhi). Hindustan Book Agency, 2010: 785–810

10. Ma X, Marinescu G. Holomorphic Morse Inequalities and Bergman Kernels. Progress in Mathematics, Vol 254. Boston, MA: Birkhäuser Boston Inc, 2007, 422 pp

    MATH  Google Scholar 

11. Ma X, Zhang W. Geometric quantization for proper moment maps. C R Math Acad Sci Paris, 2009, 347: 389–394

    Article  MathSciNet  Google Scholar 

12. Ma X, Zhang W. Geometric quantization for proper moment maps: the Vergne conjecture. Acta Math, 2014, 212(1): 11–57

    Article  MathSciNet  Google Scholar 

13. Mathai V, Zhang W. Geometric quantization for proper actions. Adv Math, 2010, 225: 1224–1247

    Article  MathSciNet  Google Scholar 

14. Meinrenken E. On Riemann-Roch formulas for multiplicities. J Amer Math Soc, 1996, 9(2): 373–389

    Article  MathSciNet  Google Scholar 

15. Meinrenken E. Symplectic surgery and the Spin^c-Dirac operator. Adv Math, 1998, 134(2): 240–277

    Article  MathSciNet  Google Scholar 

16. Meinrenken E, Sjamaar R. Singular reduction and quantization. Topology, 1999, 38: 699–762

    Article  MathSciNet  Google Scholar 

17. Paradan P-É. Localization of the Riemann-Roch character. J Funct Anal, 2001, 187(2): 442–509

    Article  MathSciNet  Google Scholar 

18. Paradan P-É. Spin^c-quantization and the K-multiplicities of the discrete series. Ann Sci Ecole Norm Sup (4), 2003, 36 (5): 805–845

    Article  MathSciNet  Google Scholar 

19. Paradan P-É. Formal geometric quantization II. Pacific J Math, 2011, 253: 169–211

    Article  MathSciNet  Google Scholar 

20. Paradan P-É, Vergne M. Equivariant Dirac operators and differentiable geometric invariant theory. Acta Math, 2017, 218: 137–199

    Article  MathSciNet  Google Scholar 

21. Souriau J-M. Structure des Systèmes Dynamiques. Maîtrises de Mathématiques. Paris: Dunod, 1970

    MATH  Google Scholar 

22. Tian Y, Zhang W. An analytic proof of the geometric quantization conjecture of Guillemin-Sternberg. Invent Math, 1998, 132(2): 229–259

    Article  MathSciNet  Google Scholar 

23. Tian Y, Zhang W. Quantization formula for symplectic manifolds with boundary. Geom Funct Anal, 1999, 9(3): 596–640

    Article  MathSciNet  Google Scholar 

24. Vergne M. Multiplicities formula for geometric quantization. I, II. Duke Math J, 1996, 82(1): 143–179, 181–194

    MathSciNet  MATH  Google Scholar 

25. Vergne M. Quantification géométrique et réduction symplectique. Astérisque, 2002, (282): 249–278

26. Vergne M. Applications of equivariant cohomology//International Congress of Mathematicians. Vol I. Zürich: Eur Math Soc, 2007: 635–664

    MATH  Google Scholar 

27. Zhang W. Holomorphic quantization formula in singular reduction. Commun Contemp Math, 1999, 1 (3): 281–293

    Article  MathSciNet  Google Scholar 

Download references