On the variety of lagrangian subalgebras, II

Evens, Sam; Lu, Jiang-Hua

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 39 (2006) no. 2, pp. 347-379.

[1] Arbarello E., Cornalba M., Griffiths P., Harris J., Geometry of Algebraic Curves, vol. 1, Springer, Berlin, 1985. | MR | Zbl

[2] Bédard R., On the Brauer liftings for modular representations, J. Algebra 93 (1985) 332-353. | MR | Zbl

[3] Belavin A., Drinfeld V., Triangular equations and simple Lie algebras, Math. Phys. Rev. 4 (1984) 93-165. | MR | Zbl

[4] Carter R., Finite Groups of Lie Type, Conjugacy Classes and Complex Characters, John Wiley & Sons, New York, 1993. | MR | Zbl

[5] De Concini C., Procesi C., Complete symmetric varieties, in: Invariant Theory, Montecatini, 1982, Lecture Notes in Math., vol. 996, Springer, Berlin, 1983, pp. 1-44. | MR | Zbl

[6] Delorme P., Classification des triples de Manin pour les algèbres de Lie réductives complexes, with an appendix by Guillaume and Macey, J. Algebra 246 (2001) 97-174. | MR | Zbl

[7] Drinfeld V.G., On Poisson homogeneous spaces of Poisson-Lie groups, Theoret. Math. Phys. 95 (2) (1993) 226-227. | MR | Zbl

[8] Evens S., Lu J.-H., Poisson harmonic forms, Kostant harmonic forms, and the $S^1$-equivariant cohomology of $K/T$, Adv. Math. 142 (1999) 171-220. | MR | Zbl

[9] Evens S., Lu J.-H., On the variety of Lagrangian subalgebras, I, Ann. École Norm. Sup. 34 (2001) 631-668. | Numdam | MR | Zbl

[10] Fomin S., Zelevinsky A., Double Bruhat cells and total positivity, J. Amer. Math. Soc. 12 (2) (1999) 335-380. | MR | Zbl

[11] Foth P., Lu J.-H., On a Poisson structure on compact symmetric spaces, Comm. Math. Phys. 251 (3) (2004) 557-566. | MR | Zbl

[12] Harris J., Algebraic Geometry, Springer, Berlin, 1995. | Zbl

[13] Hartshorne R., Algebraic Geometry, Springer, Berlin, 1977. | MR | Zbl

[14] Humphreys J., Linear Algebraic Groups, Springer, Berlin, 1981. | Zbl

[15] Karolinsky E., A Classification of Poisson Homogeneous Spaces of Complex Reductive Poisson-Lie Groups, Banach Center Publ., vol. 51, Polish Acad. Sci., Warsaw, 2000. | MR | Zbl

[16] Karolinsky E., Stolin A., Classical dynamical r-matrices, Poisson homogeneous spaces, and Lagrangian subalgebras, Lett. Math. Phys. 60 (2002) 257-274. | MR | Zbl

[17] Knapp A., Lie Groups Beyond an Introduction, Progr. Math., vol. 140, Birkhäuser, Basel, 1996. | MR | Zbl

[18] Kogan M., Zelevinsky A., On symplectic leaves and integrable systems in standard complex semi-simple Poisson-Lie groups, Int. Math. Res. Not. 32 (2002) 1685-1702. | MR | Zbl

[19] Korogodski L., Soibelman Y., Algebras of Functions on Quantum Groups, Part I, Math. Surveys Monographs, vol. 56, AMS, Providence, RI, 1998. | MR | Zbl

[20] Kostant B., Lie algebra cohomology and generalized Schubert cells, Ann. of Math. 77 (1) (1963) 72-144. | MR | Zbl

[21] Kostant B., Kumar S., The nil Hecke ring and cohomology of $G/P$ for a Kac-Moody group G, Adv. Math. 62 (3) (1986) 187-237. | MR | Zbl

[22] Lu J.-H., Coordinates on Schubert cells, Kostant’s harmonic forms, and the Bruhat Poisson structure on $G/B$, Trans. Groups 4 (4) (1998) 355-374. | MR | Zbl

[23] Lu J.-H., Classical dynamical r-matrices and homogeneous Poisson structures on $G/H$ and on $K/T$, Comm. Math. Phys. 212 (2000) 337-370. | MR | Zbl

[24] Lu J.-H., Yakimov M., On a class of double cosets in reductive algebraic groups, Int. Math. Res. Not. 13 (2005) 761-797. | MR | Zbl

[25] Lu J.-H., Yakimov M., Group orbits and regular decompositions of Poisson manifolds, in preparation.

[26] Lusztig G., Parabolic character sheaves I, Moscow Math. J. 4 (2004) 153-179. | MR | Zbl

[27] Lusztig G., Parabolic character sheaves II, Moscow Math. J. 4 (2004) 869-896. | MR | Zbl

[28] Schiffmann O., On classification of dynamical r-matrices, Math. Res. Lett. 5 (1998) 13-31. | MR | Zbl

[29] Slodowy P., Simple Singularities and Simple Algebraic Groups, Lecture Notes in Math., vol. 815, Springer, Berlin, 1980. | MR | Zbl

[30] Steinberg R., Conjugacy Classes in Algebraic Groups, Lecture Notes in Math., vol. 366, Springer, Berlin, 1974. | MR | Zbl

[31] Springer T., Intersection cohomology of $(B\times B)$-orbit closures in group compactifications, J. Algebra 258 (1) (2002) 71-111. | MR | Zbl

[32] Winter D., Algebraic group automorphisms having finite fixed point sets, Proc. Amer. Math. Soc. 18 (1967) 371-377. | MR | Zbl

[33] Yakimov M., Symplectic leaves of complex reductive Poisson Lie groups, Duke Math. J. 112 (3) (2002) 453-509. | MR | Zbl

[34] Zelevinsky A., Connected components of real double Bruhat cells, Int. Math. Res. Not. 21 (2000) 1131-1154. | MR | Zbl