Spinc-quantization and the K-multiplicities of the discrete series

Paul-Émile Paradan

Annales scientifiques de l'École Normale Supérieure (2003)

  • Volume: 36, Issue: 5, page 805-845
  • ISSN: 0012-9593

How to cite

top

Paradan, Paul-Émile. "Spinc-quantization and the K-multiplicities of the discrete series." Annales scientifiques de l'École Normale Supérieure 36.5 (2003): 805-845. <http://eudml.org/doc/82619>.

@article{Paradan2003,
author = {Paradan, Paul-Émile},
journal = {Annales scientifiques de l'École Normale Supérieure},
language = {eng},
number = {5},
pages = {805-845},
publisher = {Elsevier},
title = {Spinc-quantization and the K-multiplicities of the discrete series},
url = {http://eudml.org/doc/82619},
volume = {36},
year = {2003},
}

TY - JOUR
AU - Paradan, Paul-Émile
TI - Spinc-quantization and the K-multiplicities of the discrete series
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2003
PB - Elsevier
VL - 36
IS - 5
SP - 805
EP - 845
LA - eng
UR - http://eudml.org/doc/82619
ER -

References

top
  1. [1] Atiyah M.F., Elliptic Operators and Compact Groups, Lecture Notes in Math., vol. 401, Springer-Verlag, Berlin/New York, 1974. Zbl0297.58009MR482866
  2. [2] Atiyah M.F., Convexity and commuting Hamiltonians, Bull. London Math. Soc.14 (1982) 1-15. Zbl0482.58013MR642416
  3. [3] Atiyah M.F., Bott R., Shapiro A., Clifford modules, Topology3 (Suppl. 1) (1964) 3-38. Zbl0146.19001MR167985
  4. [4] Atiyah M.F., Segal G.B., The index of elliptic operators II, Ann. of Math.87 (1968) 531-545. Zbl0164.24201MR236951
  5. [5] Atiyah M.F., Singer I.M., The index of elliptic operators I, Ann. of Math.87 (1968) 484-530. Zbl0164.24001MR236950
  6. [6] Atiyah M.F., Singer I.M., The index of elliptic operators III, Ann. of Math.87 (1968) 546-604. Zbl0164.24301MR236952
  7. [7] Atiyah M.F., Singer I.M., The index of elliptic operators IV, Ann. of Math.93 (1971) 139-141. Zbl0212.28603MR279833
  8. [8] Berline N., Getzler E., Vergne M., Heat Kernels and Dirac Operators, Grundlehren Math. Wiss., vol. 298, Springer-Verlag, Berlin, 1991. Zbl0744.58001MR2273508
  9. [9] Berline N., Vergne M., The Chern character of a transversally elliptic symbol and the equivariant index, Invent. Math.124 (1996) 11-49. Zbl0847.46037MR1369410
  10. [10] Berline N., Vergne M., L'indice équivariant des opérateurs transversalement elliptiques, Invent. Math.124 (1996) 51-101. Zbl0883.58037MR1369411
  11. [11] Cannas da Silva A., Karshon Y., Tolman S., Quantization of presymplectic manifolds and circle actions, Trans. Amer. Math. Soc.352 (2000) 525-552. Zbl0977.53080MR1714519
  12. [12] Duflo M., Représentations de carré intégrable des groupes semi-simples réels, in: Sém. Bourbaki (1977/78), Exp. no 508, Lecture Notes in Math.710 (1979) 22-40. Zbl0411.22011MR554213
  13. [13] Duflo M., Heckman G., Vergne M., Projection d'orbites, formule de Kirillov et formule de Blattner, Mém. Soc. Math. Fr.15 (1984) 65-128. Zbl0575.22014MR789081
  14. [14] Duistermaat J.J., The Heat Lefschetz Fixed Point Formula for the Spinc-Dirac Operator, Progr. Nonlinear Differential Equation Appl., vol. 18, Birkhäuser, Boston, 1996. Zbl0858.58045MR1365745
  15. [15] Guillemin V., Sternberg S., Convexity properties of the moment mapping, Invent. Math.67 (1982) 491-513. Zbl0503.58017MR664117
  16. [16] Guillemin V., Sternberg S., Geometric quantization and multiplicities of group representations, Invent. Math.67 (1982) 515-538. Zbl0503.58018MR664118
  17. [17] Guillemin V., Sternberg S., A normal form for the moment map, in: Sternberg S. (Ed.), Differential Geometric Methods in Mathematical Physics, Reidel Publishing Company, Dordrecht, 1984. Zbl0548.58011MR767835
  18. [18] Jeffrey L., Kirwan F., Localization and quantization conjecture, Topology36 (1997) 647-693. Zbl0876.55007MR1422429
  19. [19] Harish-Chandra H., Discrete series for semi-simple Lie group, I and II, Acta Math.113 (1965) 242-318, Acta Math.116 (1966) 1-111. Zbl0199.20102MR219666
  20. [20] Hecht H., Schmid W., A proof of Blattner's conjecture, Invent. Math.31 (1975) 129-154. Zbl0319.22012MR396855
  21. [21] Kawasaki T., The index of elliptic operators over V-manifolds, Nagoya Math. J.84 (1981) 135-157. Zbl0437.58020MR641150
  22. [22] Kirwan F., Cohomology of Quotients in Symplectic and Algebraic Geometry, Princeton Univ. Press, Princeton, 1984. Zbl0553.14020MR766741
  23. [23] Kirwan F., Convexity properties of the moment mapping III, Invent. Math.77 (1984) 547-552. Zbl0561.58016MR759257
  24. [24] Kostant B., Quantization and unitary representations, in: Modern Analysis and Applications, Lecture Notes in Math., vol. 170, Springer-Verlag, Berlin/New York, 1970, pp. 87-207. Zbl0223.53028MR294568
  25. [25] Lawson H., Michelsohn M.-L., Spin Geometry, Princeton Math. Ser., vol. 38, Princeton Univ. Press, Princeton, 1989. Zbl0688.57001MR1031992
  26. [26] Lerman E., Meinrenken E., Tolman S., Woodward C., Non-Abelian convexity by symplectic cuts, Topology37 (1998) 245-259. Zbl0913.58023MR1489203
  27. [27] Meinrenken E., On Riemann–Roch formulas for multiplicities, J. Amer. Math. Soc.9 (1996) 373-389. Zbl0851.53020MR1325798
  28. [28] Meinrenken E., Symplectic surgery and the Spinc-Dirac operator, Adv. Math.134 (1998) 240-277. Zbl0929.53045MR1617809
  29. [29] Meinrenken E., Sjamaar S., Singular reduction and quantization, Topology38 (1999) 699-762. Zbl0928.37013MR1679797
  30. [30] Paradan P.-É., Formules de localisation en cohomologie équivariante, Compositio Math.117 (1999) 243-293. Zbl0934.55006MR1702424
  31. [31] Paradan P.-É., The moment map and equivariant cohomology with generalized coefficient, Topology39 (2000) 401-444. Zbl0941.37050MR1722000
  32. [32] Paradan P.-É., The Fourier transform of semi-simple coadjoint orbits, J. Funct. Anal.163 (1999) 152-179. Zbl0915.22008MR1682831
  33. [33] Paradan P.-É., Localization of the Riemann–Roch character, J. Funct. Anal.187 (2001) 442-509. Zbl1001.53062MR1875155
  34. [34] Schmid W., On a conjecture of Langlands, Ann. of Math.93 (1971) 1-42. Zbl0291.43013MR286942
  35. [35] Schmid W., L2-cohomology and the discrete series, Ann. of Math.103 (1976) 375-394. Zbl0333.22009MR396856
  36. [36] Schmid W., Discrete series, in: Proc. Symp. Pure Math., vol. 61, 1997, pp. 83-113. Zbl0936.22009MR1476494
  37. [37] Sjamaar R., Symplectic reduction and Riemann–Roch formulas for multiplicities, Bull. Amer. Math. Soc.33 (1996) 327-338. Zbl0857.58021MR1364017
  38. [38] Sjamaar R., Convexity properties of the moment mapping re-examined, Adv. Math.138 (1998) 46-91. Zbl0915.58036MR1645052
  39. [39] Segal G., Equivariant K-theory, Inst. Hautes Études Sci. Publ. Math.34 (1968) 129-151. Zbl0199.26202MR234452
  40. [40] Tian Y., Zhang W., An analytic proof of the geometric quantization conjecture of Guillemin–Sternberg, Invent. Math.132 (1998) 229-259. Zbl0944.53047MR1621428
  41. [41] Vergne M., Geometric quantization and equivariant cohomology, in: First European Congress in Mathematics, vol. 1, Progr. Math., vol. 119, Birkhäuser, Boston, 1994, pp. 249-295. Zbl0827.58020MR1341826
  42. [42] Vergne M., Multiplicity formula for geometric quantization, Part I, Part II, and Part III, Duke Math. J.82 (1996) 143-179, 181–194, 637–652. Zbl0855.58033MR1387225
  43. [43] Vergne M., Quantification géométrique et réduction symplectique, Astérisque282 (2002) 249-278. Zbl1037.53062MR1975181
  44. [44] Witten E., Two dimensional gauge theories revisited, J. Geom. Phys.9 (1992) 303-368. Zbl0768.53042MR1185834
  45. [45] Woodhouse N.M.J., Geometric Quantization, Oxford Math. Monogr., Clarendon, Oxford, 1997. Zbl0747.58004

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.