Poisson harmonic forms, Kostant harmonic forms, and the S1-equivariant cohomology of K/T

Advances in Mathematics

Volumn 142, Issue 2, 1999, Pages 171-220

  Evens, Sam ^a   Lu, Jiang Hua ^a  

^a University of Arizona   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033602348     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1006/aima.1998.1788     Document Type: Article

References (35)

1. Arabia A. CohomologieT. Bull. Soc. Math. France. 117:1989;129-165.
2. Atiyah M., Bott R. The moment map and equivariant cohomology. Topology. 23:1984;1-28.
3. Berline N., Vergne M. Fourier transforms of orbits on the coadjoint representation. Representation Theory of Reductive Groups. 1983;Birkhäuser, Basel. p. 53-68.
4. Bernstein I. N., Gelfand I. M., Gelfand S. I. Schubert cells and the cohomology of spacesGP. Russian Math Surveys. 28:1973;1-26.
5. Billey S. Kostant polynomials and the cohomology ring forGB. Proc. Nat. Acad. Sci. U.S.A. 94:1997;29-32.
6. Brylinski J.-L. A differential complex for Poisson manifolds. J. Diff. Geom. 28:1988;93-114.
7. J.-L. Brylinski, G. Zuckerman, The outer derivation of a complex Poisson manifold.
8. Drinfeld V. G. On Poisson homogeneous spaces of Poisson-Lie groups. Theo. Math. Phys. 95:1993;226-227.
9. Etingof P., Varchenko A. Geometry and classification of solutions of the classical dynamical Yang-Baxter equation. Comm. Math. Phys. 192:1998;77-120.
10. S. Evens, J.-H. Lu, A. Weinstein, Transverse measures, the modular class, and a cohomology pairing for Lie algebroids, Quart. J. Math.
11. Ginzburg V., Weinstein A. Lie Poisson structures on some Poisson Lie groups. J. Amer. Math. Soc. 5:1992;445-453.
12. Karolinsky E. The classification of Poisson homogeneous spaces of compact Poisson Lie groups (in Russian). Math. Phys. Anal. Geom. 3:1996;274-289.
13. Knapp A. Lie Groups, Lie Algebras, and Cohomology. 1988;Princeton Univ. Press, Princeton.
14. Kosmann-Schwarzbach Y. Exact Gerstenhaber algebras and Lie bialgebroids. Acta Appl. Math. 41:1995;153-165.
15. Kostant B. Lie algebra cohomology and the generalized Borel-Weil theorem. Ann. Math. 74:1961;329-387.
16. Kostant B. Lie algebra cohomology and generalized Schubert cells. Ann. Math. 77:1963;72-144.
17. Kostant B., Kumar S. The nil Hecke ring and cohomology ofGPG. Adv. Math. 62:1986;187-237.
18. Koszul J. L. Crochet de Schouten-Nijenhuis et cohomologie. Astérisque, hors série, Soc. Math. France, Paris. 1985;257-271.
19. Kumar S. The nil Hecke ring and singularity of Schubert varietes. Invent. Math. 123:1996;471-506.
20. Lichnerowicz A. Les variétés de Poisson et leurs algèbres de Lie associées. J. Diff. Geom. 12:1977;253-300.
21. Loday J.-P. Cyclic Homology. 1992;Springer-Verlag, Berlin.
22. Lu J.-H., Weinstein A. Poisson Lie groups, dressing transformations, and Bruhat decompositions. J. Differential Geom. 31:1990;501-526.
23. Lu J.-H. Poisson homogeneous spaces and Lie algebroids associated to Poisson actions. Duke Math. J. 86:1997;261-304.
24. J.-H. Lu, Coordinates on Schubert cells, Kostant's harmonic froms, and the Bruhat Poisson structure onGB.
25. J.-H. Lu, Classical dynamicalrGHKT, 1998.
26. Mathieu O. Harmonic cohomology of symplectic manifolds. Commen. Math. Helvetici. 70:1995;1-9.
27. Peterson D. Quantum cohomology ofGP. MIT lecture notes. Spring 1997.
28. Polishchuk A. Algebraic geometry of Poisson brackets. Algebraic Geometry, 7. J. Math. Sci. (New York). 84:1997;1413-1444.
29. Semenov-Tian-Shansky M. A. Dressing transformations and Poisson Lie group actions. Publ. RIMS, Kyoto University. 21:1985;1237-1260.
30. Soibelman Y. The algebra of functions on a compact quantum group and its representations. Leningrad J. 2:1991;161-178.
31. Vaisman I. Lectures on the Geometry of Poisson Manifolds. 1994;Birkhäuser, Basel.
32. Weinstein A. The modular automorphism group of a Poisson manifold. J. Geom. Phys. 23:1997;379-394.
33. Wells R. Differential Analysis on Complex Manifolds. 1973;Springer-Verlag, Berlin.
34. Yan D. Hodge structures on symplectic manifolds. Adv. Math. 120:1996;143-154.
35. P. Xu, Gerstenhaber algebras andBV.