@incollection{SB_2000-2001__43__249_0,
author = {Vergne, Mich\`ele},
title = {Quantification g\'eom\'etrique et r\'eduction symplectique},
booktitle = {S\'eminaire Bourbaki : volume 2000/2001, expos\'es 880-893},
series = {Ast\'erisque},
note = {talk:888},
pages = {249--278},
year = {2002},
publisher = {Soci\'et\'e math\'ematique de France},
number = {282},
mrnumber = {1975181},
zbl = {1037.53062},
language = {fr},
url = {https://www.numdam.org/item/SB_2000-2001__43__249_0/}
}
TY - CHAP AU - Vergne, Michèle TI - Quantification géométrique et réduction symplectique BT - Séminaire Bourbaki : volume 2000/2001, exposés 880-893 AU - Collectif T3 - Astérisque N1 - talk:888 PY - 2002 SP - 249 EP - 278 IS - 282 PB - Société mathématique de France UR - https://www.numdam.org/item/SB_2000-2001__43__249_0/ LA - fr ID - SB_2000-2001__43__249_0 ER -
%0 Book Section %A Vergne, Michèle %T Quantification géométrique et réduction symplectique %B Séminaire Bourbaki : volume 2000/2001, exposés 880-893 %A Collectif %S Astérisque %Z talk:888 %D 2002 %P 249-278 %N 282 %I Société mathématique de France %U https://www.numdam.org/item/SB_2000-2001__43__249_0/ %G fr %F SB_2000-2001__43__249_0
Vergne, Michèle. Quantification géométrique et réduction symplectique, dans Séminaire Bourbaki : volume 2000/2001, exposés 880-893, Astérisque, no. 282 (2002), Exposé no. 888, 30 p.. https://www.numdam.org/item/SB_2000-2001__43__249_0/
[1] - Elliptic operators and compact groups. Lecture Notes in Math. 401, Springer, Berlin, 1974. | Zbl | MR
[2] - Convexity and commuting Hamiltonians. Bull. London Math. Soc. 14 (1982), 1-15. | Zbl | MR
[3] & - A Lefschetz fixed-point formula for elliptic complexes, I. Ann. of Math. 86 (1967), 374-407. | Zbl | MR
[4] & - A Lefschetz fixed-point formula for elliptic complexes, II. Ann. of Math. 88 (1968), 451-491. | Zbl | MR
[5] & - The index of elliptic operators II. Ann. of Math. 87 (1968), 531-545. | Zbl | MR
[6] & - The index of ellipic operators. I. Ann. of Math. 87 (1968), 484-530. | Zbl | MR
[7] , & - Heat kernels and Dirac operators. Collection Grundlehren der Mathematischen Wissenschaften, vol. 298, Springer, Berlin, Heidelberg, New-York, 1991. | Zbl | MR
[8] - Cohomology of the Mumford quotient. math-sg/9809146.
[9] , & - Quantization of presymplectic manifolds and circle actions. Trans. Amer. Math. Soc. 352 (2000), 525-552. | Zbl | MR
[10] & - A canonical approach to multiplicity formulas for induced and restricted representations of nilpotent Lie groups. Comm. Pure Appl. Math. 41 (1988), 1051-1088. | Zbl | MR
[11] , , & - Symplectic reduction and Riemann-Roch for circle actions. Math. Res. Lett. 2 (1995), 259- 266. | Zbl | MR
[12] & - On the variation in the cohomology of the symplectic form of the reduced phase space. Invent. Math. 69 (1982), 259-268. | Zbl | MR
[13] , & - Assignments and abstract moment maps. J. Differential geom. 52 (1999), 259-301. | Zbl | MR
[14] - 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. | Zbl | MR
[15] & - Convexity properties of the moment mapping. Invent. Math. 67 (1982), 491-513. | Zbl | MR
[16] & - Geometric Quantization and Multiplicities of group representations. Invent. Math. 67 (1982), 515-538. | Zbl | MR
[17] & - Localization for non abelian group actions. Topology 34 (1995), 291-327. | Zbl | MR
[18] & - Localization and quantization conjecture. Topology 36 (1997), 647-693. | Zbl | MR
[19] - The index of elliptic operators over V-manifolds. Nagoya Math. J. 84 (1981), 135-157. | Zbl | MR
[20] - Éléments de la théorie des représentations. Traduit du russe. Éditions Mir. Moscou, 1974. | MR
[21] - Cohomology of quotients in symplectic and algebraic geometry, Princeton Univ. Press, Princeton, 1984. | Zbl | MR
[22] - Convexity properties of the moment mapping, III. Invent. Math. 77 (1984), 547-552. | Zbl | MR
[23] - Stable bundles, representation theory and Hermitian operators. Selecta Math. 4 (1998), 419-445. | Zbl | MR
[24] & - The honeycomb model of GLn(C) tensor products I : proof of the saturation conjecture. J. Amer. Math. Soc. 12 (1999), 1055-1090. | Zbl | MR
[25] - Quantization and unitary representations. In Modern analysis and applications. Lecture Notes in Math. 39 (1970), 87-207. | Zbl | MR
[26] - Symplectic cuts. Mathematical Research Letters, 1995, 2, 247-258. | Zbl | MR
[27] & - Reduction of symplectic manifolds with symmetry. Reports in Math. Phys. 5 (1974), 121-130. | Zbl | MR
[28] - On Riemann-Roch formulas for multiplicities. J. Amer. Math. Soc. 9 (1996), 373-389. | Zbl | MR
[29] - Symplectic surgery and the Spinc-Dirac operator, Advances in Math. 134 (1998), 240-277. | Zbl | MR
[30] & - Singular reduction and quantization. Topology, 38 (1999), 699-762. | Zbl | MR
[31] - 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. | Zbl | MR
[32] , & - Geometric invariant theory. 3d edition. Springer, Berlin, 1993. | Zbl | MR
[33] - Localization of the Riemann-Roch character. Journal of Functional Analysis 187 (2001), 442-509. | Zbl | MR
[34] - Spinc quantization and the K-multiplicities of the discrete series. math.DG/0103222, à paraître.
[35] - Holomorphic slices, symplectic reduction and multiplicities of group representations. Annals of Mathematics 141 (1995), 87-129. | Zbl | MR
[36] - Symplectic reduction and Riemann-Roch formulas for multiplicities. American Mathematical society Bulletin 33 (1996), 327-338. | Zbl | MR
[37] & - Stratified symplectic spaces and reduction. Annals of Mathematics 134 (1991), 375-422. | Zbl | MR
[38] - The quantization conjecture revisited. Ann. of Math. 152 (2000), 1-43. | Zbl | MR
[39] & - An analytic proof of the geometric quantization conjecture of Guillemin-Sternberg. Invent. Math. 132 (1998), 229-259. | Zbl | MR
[40] & - Quantization formula for singular reduction. Prépublication dg-ga/9706010.
[41] & - Symplectic reduction and a weighted multiplicity formula for twisted SpinC-Dirac operators. Asian Journal of Math. 2 (1998), 591- 608. | Zbl | MR
[42] & - Holomorphic Morse inequalities in symplectic reduction. Math. Res. Lett 5 (1998), 345-352. | Zbl | MR
[43] & - Quantization formula for symplectic manifolds with boundary. Geom. Funct. Anal 9 (1999), 596-640. | Zbl | MR
[44] - Equivariant index formulas for orbifolds. Duke Math. J. 82 (1996), 637-652. | Zbl | MR
[45] - Multiplicities formulas for geometric quantization. Parts I and I, Duke Math. J. 82 (1996), 143-179, 181-194. | Zbl | MR
[46] - Two dimensional gauge theories revisited. J. Geom. Phys. 9 (1992), 303-368. | Zbl | MR
[47] - The classification of transversal multiplicity-free group actions. Annals of Global Analysis and Geometry 14 (1996), 3-42. | Zbl | MR
[48] - A note on higher cohomology groups of Kähler quotients. Annals of Global Analysis and Geometry 18 (2000), 569-576. | Zbl | MR
[49] - Holomorphic quantization formula in singular reduction. Commun. Contemp. Math. 1 (1999), 281-293. | Zbl | MR
[50] - Symplectic reduction and Family quantization. International Mathematics Research Notices 19 (1999), 1043-1056. | Zbl | MR
