Multiplicities formula for geometric quantization, part I

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Multiplicities formula for geometric quantization, part I

Michele Vergne

Source: Duke Math. J. Volume 82, Number 1 (1996), 143-179.

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See also: Michele Vergne. Multiplicities formula for geometric quantization, part II. Duke Math. J. Vol. 82, No. 1 (1996), pp. 181–194.

Project Euclid: euclid.dmj/1077244843

Primary Subjects: 58F06

Secondary Subjects: 55N91, 57R20, 57S25, 58G05, 58G10

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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077244842
Mathematical Reviews number (MathSciNet): MR1387225
Zentralblatt MATH identifier: 0855.58033
Digital Object Identifier: doi:10.1215/S0012-7094-96-08206-X

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References

[1] M. F. Atiyah and R. Bott, A Lefschetz fixed point formula for elliptic complexes. I, Ann. of Math. (2) 86 (1967), 374–407.

Mathematical Reviews (MathSciNet): MR35:3701

Zentralblatt MATH: 0161.43201

Digital Object Identifier: doi:10.2307/1970694

JSTOR: links.jstor.org

[2] M. F. Atiyah and R. Bott, A Lefschetz fixed point formula for elliptic complexes. II. Applications, Ann. of Math. (2) 88 (1968), 451–491.

Mathematical Reviews (MathSciNet): MR38:731

Zentralblatt MATH: 0167.21703

Digital Object Identifier: doi:10.2307/1970721

JSTOR: links.jstor.org

[3] M. F. Atiyah and F. Hirzebruch, Vector bundles and homogeneous spaces, Proc. Sympos. Pure Math., Vol. III, American Mathematical Society, Providence, R.I., 1961, pp. 7–38.

Mathematical Reviews (MathSciNet): MR25:2617

Zentralblatt MATH: 0108.17705

[4] M. F. Atiyah and G. B. Segal, The index of elliptic operators. II, Uspehi Mat. Nauk 23 (1968), no. 6 (144), 135–149.

Mathematical Reviews (MathSciNet): MR38:5246

Zentralblatt MATH: 0164.24201

[5] M. F. Atiyah and I. M. Singer, The index of elliptic operators. I, Ann. of Math. (2) 87 (1968), 484–530.

Mathematical Reviews (MathSciNet): MR38:5243

Zentralblatt MATH: 0164.24001

Digital Object Identifier: doi:10.2307/1970715

JSTOR: links.jstor.org

[6] M. F. Atiyah and I. M. Singer, The index of elliptic operators. III, Ann. of Math. (2) 87 (1968), 546–604.

Mathematical Reviews (MathSciNet): MR38:5245

Zentralblatt MATH: 0164.24301

Digital Object Identifier: doi:10.2307/1970717

JSTOR: links.jstor.org

[7] N. Berline, E. Getzler, and M. Vergne, Heat kernels and Dirac operators, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 298, Springer-Verlag, Berlin, 1992.

Mathematical Reviews (MathSciNet): MR94e:58130

Zentralblatt MATH: 0744.58001

[8] N. Berline and M. Vergne, Classes caractéristiques équivariantes. Formule de localisation en cohomologie équivariante, C. R. Acad. Sci. Paris Sér. I Math. 295 (1982), no. 9, 539–541.

Mathematical Reviews (MathSciNet): MR83m:58002

Zentralblatt MATH: 0521.57020

[9] N. Berline and M. Vergne, The equivariant index and Kirillov's character formula, Amer. J. Math. 107 (1985), no. 5, 1159–1190.

Mathematical Reviews (MathSciNet): MR87a:58143

Zentralblatt MATH: 0604.58046

Digital Object Identifier: doi:10.2307/2374350

JSTOR: links.jstor.org

[10] J.-M. Bismut, The infinitesimal Lefschetz formulas: a heat equation proof, J. Funct. Anal. 62 (1985), no. 3, 435–457.

Mathematical Reviews (MathSciNet): MR87a:58144

Zentralblatt MATH: 0572.58021

Digital Object Identifier: doi:10.1016/0022-1236(85)90013-8

[11] J. Block and E. Getzler, Equivariant cyclic homology and equivariant differential forms, Ann. Sci. École Norm. Sup. (4) 27 (1994), no. 4, 493–527.

Mathematical Reviews (MathSciNet): MR95h:19002

Zentralblatt MATH: 0849.55008

[12] J. J. Duistermaat and G. Heckman, On the variation in the cohomology of the symplectic form of the reduced phase space, Invent. Math. 69 (1982), no. 2, 259–268.

Mathematical Reviews (MathSciNet): MR84h:58051a

Zentralblatt MATH: 0503.58015

Digital Object Identifier: doi:10.1007/BF01399506

[13] M. Duflo and M. Vergne, Cohomologie équivariante et descente, Astérisque (1993), no. 215, 5–108.

Mathematical Reviews (MathSciNet): MR95f:22018

[14] V. Guillemin, Reduced phase spaces and Riemann-Roch, Lie theory and geometry, Progr. Math., vol. 123, Birkhäuser Boston, Boston, MA, 1994, pp. 305–334.

Mathematical Reviews (MathSciNet): MR96m:58095

Zentralblatt MATH: 0869.58017

[15] V. Guillemin, E. Lerman, and S. Sternberg, On the Kostant multiplicity formula, J. Geom. Phys. 5 (1988), no. 4, 721–750 (1989).

Mathematical Reviews (MathSciNet): MR92f:58058

Zentralblatt MATH: 0713.58013

Digital Object Identifier: doi:10.1016/0393-0440(88)90026-5

[16] V. Guillemin and E. Prato, Heckman, Kostant, and Steinberg formulas for symplectic manifolds, Adv. Math. 82 (1990), no. 2, 160–179.

Mathematical Reviews (MathSciNet): MR91h:58041

Zentralblatt MATH: 0718.58027

Digital Object Identifier: doi:10.1016/0001-8708(90)90087-4

[17] V. Guillemin and S. Sternberg, Geometric quantization and multiplicities of group representations, Invent. Math. 67 (1982), no. 3, 515–538.

Mathematical Reviews (MathSciNet): MR83m:58040

Zentralblatt MATH: 0503.58018

Digital Object Identifier: doi:10.1007/BF01398934

[18] J. Kalkman, Cohomology rings of symplectic quotients, J. Reine Angew. Math. 458 (1995), 37–52.

Mathematical Reviews (MathSciNet): MR96a:55014

Zentralblatt MATH: 0851.57029

Digital Object Identifier: doi:10.1515/crll.1995.458.37

[19] L. C. Jeffrey and F. C. Kirwan, Localization for nonabelian group actions, Topology 34 (1995), no. 2, 291–327.

Mathematical Reviews (MathSciNet): MR97g:58057

Zentralblatt MATH: 0833.55009

Digital Object Identifier: doi:10.1016/0040-9383(94)00028-J

[20] L. C. Jeffrey and F. C. Kirwan, On localization and Riemann-Roch numbers for symplectic quotients, preprint.

Mathematical Reviews (MathSciNet): MR1397936

Zentralblatt MATH: 0870.53022

Digital Object Identifier: doi:10.1093/qmath/47.2.165

[21] B. Kostant, Quantization and unitary representations. I. Prequantization, Lectures in modern analysis and applications, III, Springer, Berlin, 1970, 87–208. Lecture Notes in Math., Vol. 170.

Mathematical Reviews (MathSciNet): MR45:3638

Zentralblatt MATH: 0223.53028

Digital Object Identifier: doi:10.1007/BFb0079068

[22] E. Meinrenken, On Riemann-Roch formulas for multiplicities, preprint, 1994.

Mathematical Reviews (MathSciNet): MR1325798

Zentralblatt MATH: 0851.53020

Digital Object Identifier: doi:10.1090/S0894-0347-96-00197-X

JSTOR: links.jstor.org

[23] J. H. Rawnsley and P. L. Robinson, The metaplectic representation, $\rm Mp\sp c$ structures and geometric quantization, Mem. Amer. Math. Soc. 81 (1989), no. 410, iv+92.

Mathematical Reviews (MathSciNet): MR91b:58083

Zentralblatt MATH: 0681.22022

[24] P. L. Robinson, Metaplectic reduction, J. London Math. Soc. (2) 46 (1992), no. 2, 375–384.

Mathematical Reviews (MathSciNet): MR93g:58052

Zentralblatt MATH: 0769.58028

Digital Object Identifier: doi:10.1112/jlms/s2-46.2.375

[25] J. M. Souriau, Structure des systèmes dynamiques, Maitrises de mathématiques, Dunod, Paris, 1970.

Mathematical Reviews (MathSciNet): MR41:4866

Zentralblatt MATH: 0186.58001

[26] M. Vergne, Sur l'indice des opérateurs transversalement elliptiques, C. R. Acad. Sci. Paris Sér. I Math. 310 (1990), no. 6, 329–332.

Mathematical Reviews (MathSciNet): MR91a:58180

Zentralblatt MATH: 0693.58022

[27] M. Vergne, Geometric quantization and equivariant cohomology, First European Congress of Mathematics, Vol. I (Paris, 1992), Progr. Math., vol. 119, Birkhäuser, Basel, 1994, pp. 249–295.

Mathematical Reviews (MathSciNet): MR96j:58074

Zentralblatt MATH: 0827.58020

[28] M. Vergne, A note on the Jeffrey-Kirwan-Witten localisation formula, to appear in Topology.

Mathematical Reviews (MathSciNet): MR1367283

Digital Object Identifier: doi:10.1016/0040-9383(95)00007-0

[29] M. Vergne, Quantification géométrique et multiplicités, C. R. Acad. Sci. Paris Sér. I Math. 319 (1994), no. 4, 327–332.

Mathematical Reviews (MathSciNet): MR96d:58057

Zentralblatt MATH: 0814.58020

[30a] M. Vergne, Multiplicities formula for geometric quantization. I, Duke Math. J. 82 (1996), no. 1, 143–179.

Mathematical Reviews (MathSciNet): MR98e:58087

Zentralblatt MATH: 0855.58033

Digital Object Identifier: doi:10.1215/S0012-7094-96-08206-X

Project Euclid: euclid.dmj/1077244842

[30b] M. Vergne, Multiplicities formula for geometric quantization. II, Duke Math. J. 82 (1996), no. 1, 181–194.

Mathematical Reviews (MathSciNet): MR98e:58087

Zentralblatt MATH: 0855.58034

Digital Object Identifier: doi:10.1215/S0012-7094-96-08206-X

Project Euclid: euclid.dmj/1077244842

[31] E. Witten, Two-dimensional gauge theories revisited, J. Geom. Phys. 9 (1992), no. 4, 303–368.

Mathematical Reviews (MathSciNet): MR93m:58017

Zentralblatt MATH: 0768.53042

Digital Object Identifier: doi:10.1016/0393-0440(92)90034-X

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