Quantification géométrique et réduction symplectique
Séminaire Bourbaki : volume 2000/2001, exposés 880-893, Astérisque, no. 282 (2002), Talk no. 888, 30 p. 
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Vergne, Michèle. Quantification géométrique et réduction symplectique, in Séminaire Bourbaki : volume 2000/2001, exposés 880-893, Astérisque, no. 282 (2002), Talk no. 888, 30 p. http://archive.numdam.org/item/SB_2000-2001__43__249_0/

[1] M. F. Atiyah - Elliptic operators and compact groups. Lecture Notes in Math. 401, Springer, Berlin, 1974. | MR | Zbl

[2] M. F. Atiyah - Convexity and commuting Hamiltonians. Bull. London Math. Soc. 14 (1982), 1-15. | MR | Zbl

[3] M. F. Atiyah & R. Bott - A Lefschetz fixed-point formula for elliptic complexes, I. Ann. of Math. 86 (1967), 374-407. | MR | Zbl

[4] M. F. Atiyah & R. Bott - A Lefschetz fixed-point formula for elliptic complexes, II. Ann. of Math. 88 (1968), 451-491. | MR | Zbl

[5] M. F. Atiyah & G. B. Segal - The index of elliptic operators II. Ann. of Math. 87 (1968), 531-545. | MR | Zbl

[6] M. F. Atiyah & I. M. Singer - The index of ellipic operators. I. Ann. of Math. 87 (1968), 484-530. | MR | Zbl

[7] N. Berline, E. Getzler & M. Vergne - Heat kernels and Dirac operators. Collection Grundlehren der Mathematischen Wissenschaften, vol. 298, Springer, Berlin, Heidelberg, New-York, 1991. | MR | Zbl

[8] M. Braverman - Cohomology of the Mumford quotient. math-sg/9809146.

[9] A. Canas Da Silva, Y. Karshon & S. Tolman - Quantization of presymplectic manifolds and circle actions. Trans. Amer. Math. Soc. 352 (2000), 525-552. | MR | Zbl

[10] L. Corwin & F. P. Greenleaf - A canonical approach to multiplicity formulas for induced and restricted representations of nilpotent Lie groups. Comm. Pure Appl. Math. 41 (1988), 1051-1088. | MR | Zbl

[11] J. J. Duistermaat, V. Guillemin, E. Meinrenken & S. Wu - Symplectic reduction and Riemann-Roch for circle actions. Math. Res. Lett. 2 (1995), 259- 266. | MR | Zbl

[12] J. J. Duistermaat & G. Heckman - On the variation in the cohomology of the symplectic form of the reduced phase space. Invent. Math. 69 (1982), 259-268. | MR | Zbl

[13] V. L. Ginzburg, V. Guillemin & Y. Karshon - Assignments and abstract moment maps. J. Differential geom. 52 (1999), 259-301. | MR | Zbl

[14] V. Guillemin - Reduced phase spaces and Riemann-Roch. in Proceedings : Lie Groups and Geometry in honor of B. Kostant (Massachusets of Technology, 1994. Progress in Math. 123, Birkhäuser, Boston (1995), 305-334. | MR | Zbl

[15] V. Guillemin & S. Sternberg - Convexity properties of the moment mapping. Invent. Math. 67 (1982), 491-513. | MR | Zbl

[16] V. Guillemin & S. Sternberg - Geometric Quantization and Multiplicities of group representations. Invent. Math. 67 (1982), 515-538. | MR | Zbl

[17] L. C. Jeffrey & F. C. Kirwan - Localization for non abelian group actions. Topology 34 (1995), 291-327. | MR | Zbl

[18] L. C. Jeffrey & F. C. Kirwan - Localization and quantization conjecture. Topology 36 (1997), 647-693. | MR | Zbl

[19] T. Kawasaki - The index of elliptic operators over V-manifolds. Nagoya Math. J. 84 (1981), 135-157. | MR | Zbl

[20] A. A. Kirillov - Éléments de la théorie des représentations. Traduit du russe. Éditions Mir. Moscou, 1974. | MR

[21] F. C. Kirwan - Cohomology of quotients in symplectic and algebraic geometry, Princeton Univ. Press, Princeton, 1984. | MR | Zbl

[22] F. C. Kirwan - Convexity properties of the moment mapping, III. Invent. Math. 77 (1984), 547-552. | MR | Zbl

[23] Klyachko - Stable bundles, representation theory and Hermitian operators. Selecta Math. 4 (1998), 419-445. | MR | Zbl

[24] A. Knutson & T. Tao - The honeycomb model of GLn(C) tensor products I : proof of the saturation conjecture. J. Amer. Math. Soc. 12 (1999), 1055-1090. | MR | Zbl

[25] B. Kostant - Quantization and unitary representations. In Modern analysis and applications. Lecture Notes in Math. 39 (1970), 87-207. | MR | Zbl

[26] E. Lerman - Symplectic cuts. Mathematical Research Letters, 1995, 2, 247-258. | MR | Zbl

[27] J. Marsden & A. Weinstein - Reduction of symplectic manifolds with symmetry. Reports in Math. Phys. 5 (1974), 121-130. | MR | Zbl

[28] E. Meinrenken - On Riemann-Roch formulas for multiplicities. J. Amer. Math. Soc. 9 (1996), 373-389. | MR | Zbl

[29] E. Meinrenken - Symplectic surgery and the Spinc-Dirac operator, Advances in Math. 134 (1998), 240-277. | MR | Zbl

[30] E. Meinrenken & R. Sjamaar - Singular reduction and quantization. Topology, 38 (1999), 699-762. | MR | Zbl

[31] D. Mumford - Proof of the convexity theorem. Appendix to : Stratification of the null cone via the moment map, by L. Ness. Amer. J. Math. 106 (1984), 1280-1329. | MR | Zbl

[32] D. Mumford, J. Fogarty & F. Kirwan - Geometric invariant theory. 3d edition. Springer, Berlin, 1993. | MR | Zbl

[33] P.-E. Paradan - Localization of the Riemann-Roch character. Journal of Functional Analysis 187 (2001), 442-509. | MR | Zbl

[34] P.-E. Paradan - Spinc quantization and the K-multiplicities of the discrete series. math.DG/0103222, à paraître.

[35] R. Sjamaar - Holomorphic slices, symplectic reduction and multiplicities of group representations. Annals of Mathematics 141 (1995), 87-129. | MR | Zbl

[36] R. Sjamaar - Symplectic reduction and Riemann-Roch formulas for multiplicities. American Mathematical society Bulletin 33 (1996), 327-338. | MR | Zbl

[37] R. Sjamaar & E. Lerman - Stratified symplectic spaces and reduction. Annals of Mathematics 134 (1991), 375-422. | MR | Zbl

[38] C. Teleman - The quantization conjecture revisited. Ann. of Math. 152 (2000), 1-43. | MR | Zbl

[39] Y. Tian & W. Zhang - An analytic proof of the geometric quantization conjecture of Guillemin-Sternberg. Invent. Math. 132 (1998), 229-259. | MR | Zbl

[40] Y. Tian & W. Zhang - Quantization formula for singular reduction. Prépublication dg-ga/9706010.

[41] Y. Tian & W. Zhang - Symplectic reduction and a weighted multiplicity formula for twisted SpinC-Dirac operators. Asian Journal of Math. 2 (1998), 591- 608. | MR | Zbl

[42] Y. Tian & W. Zhang - Holomorphic Morse inequalities in symplectic reduction. Math. Res. Lett 5 (1998), 345-352. | MR | Zbl

[43] Y. Tian & W. Zhang - Quantization formula for symplectic manifolds with boundary. Geom. Funct. Anal 9 (1999), 596-640. | MR | Zbl

[44] M. Vergne - Equivariant index formulas for orbifolds. Duke Math. J. 82 (1996), 637-652. | MR | Zbl

[45] M. Vergne - Multiplicities formulas for geometric quantization. Parts I and I, Duke Math. J. 82 (1996), 143-179, 181-194. | MR | Zbl

[46] E. Witten - Two dimensional gauge theories revisited. J. Geom. Phys. 9 (1992), 303-368. | MR | Zbl

[47] C. Woodward - The classification of transversal multiplicity-free group actions. Annals of Global Analysis and Geometry 14 (1996), 3-42. | MR | Zbl

[48] S. Wu - A note on higher cohomology groups of Kähler quotients. Annals of Global Analysis and Geometry 18 (2000), 569-576. | MR | Zbl

[49] W. Zhang - Holomorphic quantization formula in singular reduction. Commun. Contemp. Math. 1 (1999), 281-293. | MR | Zbl

[50] W. Zhang - Symplectic reduction and Family quantization. International Mathematics Research Notices 19 (1999), 1043-1056. | MR | Zbl