Duistermaat-Heckman measures in a non-compact setting

Elisa Prato; Siye Wu

Compositio Mathematica (1994)

  • Volume: 94, Issue: 2, page 113-128
  • ISSN: 0010-437X

How to cite


Prato, Elisa, and Wu, Siye. "Duistermaat-Heckman measures in a non-compact setting." Compositio Mathematica 94.2 (1994): 113-128. <http://eudml.org/doc/90331>.

author = {Prato, Elisa, Wu, Siye},
journal = {Compositio Mathematica},
keywords = {Hamiltonian action; moment map; Duistermaat-Heckman formula},
language = {eng},
number = {2},
pages = {113-128},
publisher = {Kluwer Academic Publishers},
title = {Duistermaat-Heckman measures in a non-compact setting},
url = {http://eudml.org/doc/90331},
volume = {94},
year = {1994},

AU - Prato, Elisa
AU - Wu, Siye
TI - Duistermaat-Heckman measures in a non-compact setting
JO - Compositio Mathematica
PY - 1994
PB - Kluwer Academic Publishers
VL - 94
IS - 2
SP - 113
EP - 128
LA - eng
KW - Hamiltonian action; moment map; Duistermaat-Heckman formula
UR - http://eudml.org/doc/90331
ER -


  1. [A] M.F. Atiyah, Convexity and commuting Hamiltonians, Bull. London Math. Soc.14 (1982), 1-15. Zbl0482.58013MR642416
  2. [BV] N. Berline, M. Vergne, Classes caractéristiques équivariantes, formule de localisation en cohomologie équivariante, Comptes Rendus Acad. Sc. Paris295 (1982), 539-541; Zéros d'un champ de vecteurs et classes caractéristiques équivariantes, Duke Math. J.50 (1983), 539-549. Zbl0515.58007MR685019
  3. [CDM-HNP] M. Condevaux, P. Dazord and P. Molino, Géométrie du moment, In Travaux du Séminaire Sud-Rodanien de Géométrie I, Publ. Dép. Math. Nouvelle Sér. B88-1, Univ. Claude-Bernard, Lyon (1988), pp. 131-160; MR1040871
  4. J. Hilgert, K.-H. Neeb and W. Plank, Symplectic convexity theorems and coadjoint orbits, preprint 1993. Zbl0819.22006MR1270171
  5. [DHV] M. Duflo, G. Heckman and M. Vergne, Projection d'orbites, formule de Kirillov et formule de Blattner, Mem. Soc. Math. France15 (1984), 65-128. Zbl0575.22014MR789081
  6. [DH] J.J. Duistermaat and G.J. Heckman, On the variation in the cohomology of the symplectic form of the reduced phase space,Invent. Math.69 (1982), 259-268; Addendum, ibid. 72 (1983), 153-158. Zbl0503.58016MR674406
  7. [F-L-B] W. Fenchel, Convex cones, sets, and functions, Princeton University lecture notes (1953); Zbl0053.12203
  8. S.R. Lay, Convex sets and their applications, John Wiley & Sons, New York, Chichester, Brisbane, 1982, Chap. 8; Zbl0492.52001MR655598
  9. A. Brøndsted, An introduction to convex polytopes, Springer-Verlag, New York, Heidelberg, Berlin, 1983, §8. Zbl0509.52001MR683612
  10. [GLS] V. Guillemin, E. Lerman and S. Sternberg, On the Kostant multiplicity formula, J. Geom. Phys.5 (1988), 721-750. Zbl0713.58013MR1075729
  11. [GP] V. Guillemin and E. Prato, Heckman, Kostant, and Steinberg formulas for symplectic manifolds, Adv. Math.82 (1990), 160-179. Zbl0718.58027MR1063956
  12. [GS] V. Guillemin and S. Sternberg, Symplectic techniques in physics, Cambridge University Press, Cambridge, New York, Melbourne, 1990, §II.27. Zbl0734.58005MR1066693
  13. [H] G. Heckman, Projection of orbits and asymptotic behaviour of multiplicities for compact connected Lie groups, Invent. Math.67 (1982), 333-356. Zbl0497.22006MR665160
  14. [He] S. Helgason, Differential geometry, Lie groups and symmetric spaces, Academic Press, Orlando, San Diego, New York, 1978, Chap. VIII. Zbl0451.53038MR514561
  15. [Hö] L. Hörmander, The analysis of linear partial differential operatorsI, 2nd ed., Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1990, §7.4. MR404822
  16. [HC1] Harish-Chandra, Invariant differential operators on a semi-simple Lie algebra, Proc. Nat. Acad. Sci. U. S. A.42 (1956), 252-253. Zbl0072.02001MR80260
  17. [HC2] Harish-Chandra, Representations of semisimple Lie groups IV, Amer. J. Math.77 (1955), 743-777. Zbl0066.35603MR72427
  18. [JK] L.C. Jeffrey and F.C. Kirwan, Localization for nonabelian group actions, preprint, alg-geom/9307001, 1993. MR1318878
  19. [K1] A. Knapp, Bounded symmetric domains and holomorphic discrete series, Symmetric spaces, Eds. W. M. Boothby and G. L. Weiss, Marcel Dekker, Inc., New York, 1972, pp.211-246. Zbl0242.32022MR460544
  20. [K2] A. Knapp, Representation theory of semisimple Lie groups, Princeton University Press, Princeton, 1986, Chap. VI. Zbl0604.22001MR855239
  21. [P] E. Prato, Convexity properties of the moment map for certain non-compact manifolds, preprint (1992), to appear in Comm. Anal. Geom. Zbl0842.58034MR1312689
  22. [W] S. Wu, An integration formula for the square of moment maps of circle actions, Lett. Math. Phys.29 (1993), 311-328. Zbl0793.53035MR1257832

NotesEmbed ?


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.