On the variety of lagrangian subalgebras, I
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 34 (2001) no. 5, pp. 631-668. 
@article{ASENS_2001_4_34_5_631_0,
     author = {Evens, Sam and Lu, Jiang-Hua},
     title = {On the variety of lagrangian subalgebras, {I}},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {631--668},
     publisher = {Elsevier},
     volume = {Ser. 4, 34},
     number = {5},
     year = {2001},
     doi = {10.1016/s0012-9593(01)01072-2},
     mrnumber = {1862022},
     zbl = {1098.17006},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/s0012-9593(01)01072-2/}
}
TY  - JOUR
AU  - Evens, Sam
AU  - Lu, Jiang-Hua
TI  - On the variety of lagrangian subalgebras, I
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 2001
SP  - 631
EP  - 668
VL  - 34
IS  - 5
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/s0012-9593(01)01072-2/
DO  - 10.1016/s0012-9593(01)01072-2
LA  - en
ID  - ASENS_2001_4_34_5_631_0
ER  - 
%0 Journal Article
%A Evens, Sam
%A Lu, Jiang-Hua
%T On the variety of lagrangian subalgebras, I
%J Annales scientifiques de l'École Normale Supérieure
%D 2001
%P 631-668
%V 34
%N 5
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/s0012-9593(01)01072-2/
%R 10.1016/s0012-9593(01)01072-2
%G en
%F ASENS_2001_4_34_5_631_0
Evens, Sam; Lu, Jiang-Hua. On the variety of lagrangian subalgebras, I. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 34 (2001) no. 5, pp. 631-668. doi : 10.1016/s0012-9593(01)01072-2. http://archive.numdam.org/articles/10.1016/s0012-9593(01)01072-2/

[1] Adams J., Barbasch D., Vogan D., The Langlands Classification and Irreducible Characters for Real Reductive Groups, Birkhäuser, 1992. | MR | Zbl

[2] Arbarello E., Cornalba M., Griffiths P., Harris J., Geometry of Algebraic Curves, Vol. 1, Springer-Verlag, 1985. | MR | Zbl

[3] Borel A., De Siebenthal J., Les sous-groupes fermes de rang maximum des groupes de Lie clos, Comment. Math. Helv. 23 (1949) 200-221. | MR | Zbl

[4] De Concini C., Procesi C., Complete symmetric varieties, in: Invariant Theory (Montecatini, 1982), Lect. Notes in Math., 996, Springer, Berlin, New York, 1983, pp. 1-44. | MR | Zbl

[5] Delorme P., Classification des triples de Manin pour les algèbres de Lie réductives complexes, math.QA/0003123.

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

[7] Evens S., Lu J.-H., Poisson harmonic forms, Kostant harmonic forms, and the S1-equivariant cohomology of K/T, Adv. Math. 142 (1999) 171-220. | MR | Zbl

[8] Etingof P., Varchenko A., Geometry and classification of solutions of the classical dynamical Yang-Baxter equation, Comm. Math. Phys. 192 (1998) 177-220. | Zbl

[9] Hartshorne R., Algebraic Geometry, Springer-Verlag, 1977. | MR | Zbl

[10] Helgason S., Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, 1978. | MR | Zbl

[11] Humphreys J., Introduction to Lie Algebras and Representation Theory, Springer-Verlag, 1972. | MR | Zbl

[12] Karolinsky E., The classification of Poisson homogeneous spaces of compact Poisson Lie groups, Mathematical Physics, Analysis, and Geometry 3 (3/4) (1996) 274-289, (in Russian).

[13] Karolinsky E., A classification of Poisson homogeneous spaces of complex reductive Poisson-Lie groups, Banach Center Publ., 51, Polish Academy of Sciences, Warsaw, 2000. | Zbl

[14] Korogodski L., Soibelman Y., Algebras of Functions on Quantum Groups, Part I, Mathematical Surveys and Monographs, 56, American Mathematical Society, 1998. | MR | Zbl

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

[16] 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. | Zbl

[17] Lu J.-H., Weinstein A., Poisson Lie groups, dressing transformations, and Bruhat decompositions, J. Differential Geom. 31 (1990) 501-526. | MR | Zbl

[18] Lu J.-H., Multiplicative and affine Poisson structures on Lie groups, PhD thesis, University of California, Berkeley, 1990.

[19] Lu J.-H., Poisson homogeneous spaces and Lie algebroids associated to Poisson actions, Duke Math. J. 86 (2) (1997) 261-304. | MR | Zbl

[20] Lu J.-H., Coordinates on Schubert cells, Kostant's harmonic forms, and the Bruhat Poisson structure on G/B, Trans. Groups 4 (4) (1999) 355-374. | MR | Zbl

[21] 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

[22] Onishchik A.L., Vinberg E.B. (Eds.), Structure of Lie Groups and Lie Algebras, Lie Groups and Lie Algebras III, Encyclopaedia of Mathematical Sciences, 41, Springer-Verlag, Berlin, 1994. | MR | Zbl

[23] Oshima T., Sekiguchi J., Eigenspaces of invariant differential operators on an affine symmetric space, Invent. Math. 57 (1980) 1-81. | EuDML | MR | Zbl

[24] Panov A., Manin triples of real simple Lie algebras, part 1, available as math.QA/9904156.

[25] Panov A., Manin triples of real simple Lie algebras, part 2, available as math.QA/9905028.

[26] Porteous I., Clifford Algebras and the Classical Groups, Cambridge University Press, 1995. | MR | Zbl

[27] Rossman W., The structure of semi-simple symmetric spaces, Canadian Math. J. 31 (1979) 157-180.

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

[29] Schlichtkrull H., Hyperfunctions and Harmonic Analysis on Symmetric Spaces, Birkhäuser, 1984. | MR | Zbl

[30] Silhol R., Real Algebraic Surfaces, Lect. Notes in Math., 1392, Springer-Verlag, 1989. | MR | Zbl

Cité par Sources :