Construction d'un groupe de Kac-Moody et applications

Olivier Mathieu

Compositio Mathematica (1989)

  • Volume: 69, Issue: 1, page 37-60
  • ISSN: 0010-437X

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Mathieu, Olivier. "Construction d'un groupe de Kac-Moody et applications." Compositio Mathematica 69.1 (1989): 37-60. <http://eudml.org/doc/89941>.

@article{Mathieu1989,
author = {Mathieu, Olivier},
journal = {Compositio Mathematica},
keywords = {projective normality; generalized Cartan matrix; ind-group scheme; Borel subgroup scheme; Schubert variety; PRV-conjecture; symmetrizable Kac- Moody algebras; Frobenius splitting},
language = {fre},
number = {1},
pages = {37-60},
publisher = {Kluwer Academic Publishers},
title = {Construction d'un groupe de Kac-Moody et applications},
url = {http://eudml.org/doc/89941},
volume = {69},
year = {1989},
}

TY - JOUR
AU - Mathieu, Olivier
TI - Construction d'un groupe de Kac-Moody et applications
JO - Compositio Mathematica
PY - 1989
PB - Kluwer Academic Publishers
VL - 69
IS - 1
SP - 37
EP - 60
LA - fre
KW - projective normality; generalized Cartan matrix; ind-group scheme; Borel subgroup scheme; Schubert variety; PRV-conjecture; symmetrizable Kac- Moody algebras; Frobenius splitting
UR - http://eudml.org/doc/89941
ER -

References

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  1. 1 H.H. Andersen: Schubert varieties and Demazure's character formula. Inv. Math.79 (1985) 611-617. Zbl0591.14036
  2. 2 M. Demazure: Désignularisation des variétés de Schubert généralisées. Ann. Scient. Ec. Norm. Sup. 4ème série, 7 (1974) 53-88. Zbl0312.14009MR354697
  3. 3 A. Joseh: On the Demazure charater formula. Ann. Ec. Norm. Sup. 4ème série, 18 (1985) 389-419. Zbl0589.22014MR826100
  4. 4 V.G. Kac: Infinite dimensional Lie algebras. Progress in Math44, Birkhauser, Basel, Boston, Stuttgard (1983). Zbl0537.17001MR739850
  5. 5 V.G. Kac and D. Peterson: Regular functions on certain infinite dimensional groups. Arithmetic and Geometry. Progress in Math36 (1983) 141-146Birkhauser, Boston. Zbl0578.17014MR717610
  6. 6 S. Kumar: Demazure character formula in arbitrary Kac-Moody setting. Inv. Math.89 (1987) 423. Zbl0635.14023MR894387
  7. 7 S. Kumar: Proof of the Parathasarathy-Ranga Rao-Varadarajan conjecture. Preprint (1987). Zbl0668.17008MR943925
  8. 8 O. Mathieu: Fromule de Weyl et de Demazure, et théorème de Borel-Weil Bott pour les algèbres de Kac-Moody générales. Preprint (1986). Zbl0602.17008
  9. 9 O. Mathieu: Fibrés en droite sur les variétés de Schubert associées aux algèbres de Kac-Moody. Proceeding de "Symposium on topological methods in field theory" (Helsinki-Juin 1986) Scientific World. Zbl0642.17011MR1026484
  10. 10 O. Mathieu: Formule de Demazure-Weyl... Comptes Rendus 303, série I (1986) 391-394. Zbl0602.17008MR862200
  11. 11 O. Mathieu: Construction du groupe associé aux algèbres de Kac-Moody. Comptes Rendus 306 série I (1988) 227-230. Zbl0666.17006MR932325
  12. 12 V.B. Metha and A. Ramanathan: Frobenius splitting and cohomology for Schubert varieties. Ann of Math.122 (1985) 27-40. Zbl0601.14043MR799251
  13. 13 K.R. Parthasarathy, R. Ranga Rao and V.S. Varadarajan: Representations of complex Lie groups and Lie algebras. Ann of Math.85 (1967) 383-429. Zbl0177.18004MR225936
  14. 14 P. Polo: Variétés de Schubert et excellentes filtrations. Preprint (1987). MR1021515
  15. 15 S. Ramanan and A. Ramanathan: Projective normality of flag varieties and Schubert varieties. Inv. Math.79 (1985) 217-224. Zbl0553.14023MR778124
  16. 16 A. Ramanathan: Equations defining Schubert varieties and Frobenius splitting of the diagonal (preprint). Zbl0634.14035
  17. 17 C.S. Seshadri: Normality of Schubert variety. Proceeding de "Algebraic Geometry" (Bombay, Avril 1984). 
  18. 18 P. Slodowy: On the geometry of Schubert varieties attached to Kac-Moody Lie algebras. Proceeding de "Algebraic Geometry" (Vancouver, Juillet 1984). Zbl0591.14038
  19. 19 J. Tits: Algèbres de Kac-Moody et groupes associés. Annuaire du Collège de France (1980-1981) 75-87 et (1981-1982) 91-106. 
  20. 20 J. Tits: Groups and groups functors attached to Kac-Moody data. Arbeitstagung, Bonn1984, Springer Verlag LN1111 (1985) 193-223. Zbl0572.17010MR797422

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