Infinite grassmannians and moduli spaces of G-bundles

  • Shrawan Kumar
Chapter
First Online:
Part of the Lecture Notes in Mathematics book series (LNM, volume 1649)

Keywords

Modulus Space Vector Bundle Line Bundle Schubert Variety Flag Variety 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AM] Atiyah, M.F. and Macdonald, I.G., Introduction to Commutative Algebra, Addison-Wesley, 1969.Google Scholar
  2. [BL] Beauville, A. and Laszlo, Y., Conformal blocks and generalized theta functions, Commun. Math. Phys. 164, 385–419, (1994).MathSciNetCrossRefMATHGoogle Scholar
  3. [BL2] Beauville, A. and Laszlo, Y., Un lemme de descente, C.R. Acad. Sci. Paris 320, 335–340, (1995).MathSciNetGoogle Scholar
  4. [B] Borel, A., Linear Algebraic Groups, W.A. Benjamin, New York, 1969.MATHGoogle Scholar
  5. [Bo] Bourbaki, N., Groupes et Algèbres de Lie, Chap. 4–6, Masson, Paris, 1981.MATHGoogle Scholar
  6. [DN] Drezet, J.-M. and Narasimhan, M.S., Groupe de Picard des variétés de modules de fibrés semi-stables sur les courbes algébriques, Invent. Math. 97, 53–94, (1989).MathSciNetCrossRefMATHGoogle Scholar
  7. [D] Dynkin, E.B., Semisimple subalgebras of semisimple Lie algebras, Am. Math. Soc. Transl. (Ser. II) 6, 111–244, (1957).CrossRefMATHGoogle Scholar
  8. [Fa] Faltings, G., A proof for the Verlinde formula, J. Alg. Geom. 3, 347–374, (1994).MathSciNetMATHGoogle Scholar
  9. [F] Fulton, W., Introduction to Intersection Theory in Algebraic Geometry, Reg. Conf. Ser. in Math., number 54, AMS, Providence, RI, 1984.CrossRefGoogle Scholar
  10. [G] Grothendieck, A., Éléments de géométrie algébrique IV (Seconde Partie), Publications Math. IHES 24, (1965).Google Scholar
  11. [GK] Guruprasad, K. and Kumar, S., A new geometric invariant associated to the space of flat connections, Compositio Math. 73, 199–222, (1990).MathSciNetMATHGoogle Scholar
  12. [H1] Harder, G., Halbeinfache gruppenschemata über Dedekindringen, Invent. Math. 4, 165–191, (1967).MathSciNetCrossRefMATHGoogle Scholar
  13. [H2] Harder, G., Halbeinfache gruppenschemata über vollständigen kurven, Invent. Math. 6, 107–149, (1968).MathSciNetCrossRefMATHGoogle Scholar
  14. [Ha] Hartshorne, R., Algebraic Geometry, Berlin-Heidelberg-New York, Springer, 1977.CrossRefMATHGoogle Scholar
  15. [Hu] Humphreys, J.E., Introduction to Lie Algebras and Representation Theory, Graduate Texts in Math., vol. 9, Berlin-Heidelberg-New York, Springer, 1972.MATHGoogle Scholar
  16. [Hur] Hurtubise, J.C., Holomorphic maps of a Riemann surface into a flag manifold, J. of Diff. Geom. 43, 99–118, (1996).MathSciNetMATHGoogle Scholar
  17. [IM] Iwahori, N. and Matsumoto, H., On some Bruhat decomposition and the structure of the Hecke rings of p-adic Chevalley groups, Publ. Math. IHES 25, 237–280, (1965).MathSciNetCrossRefMATHGoogle Scholar
  18. [K] Kac, V.G., Infinite Dimensional Lie Algebras, Third edition, Cambridge, Cambridge University Press, 1990.CrossRefMATHGoogle Scholar
  19. [KL] Kazhdan, D. and Lusztig, G., Schubert varieties and Poincare duality, Proc. Symp. Pure Math. (A.M.S.) 36, 185–203, (1980).MathSciNetCrossRefMATHGoogle Scholar
  20. [KL2] Kazhdan, D. and Lusztig, G., Tensor structures arising from affine Lie algebras, J. of A.M.S. 6, 905–947, (1993).MathSciNetMATHGoogle Scholar
  21. [Ku1] Kumar, S., Demazure character formula in arbitrary Kac-Moody setting, Invent Math. 89, 395–423, (1987).MathSciNetCrossRefMATHGoogle Scholar
  22. [Ku2] Kumar, S., Normality of certain Springer fibers, (handwritten notes), 1986.Google Scholar
  23. [KNR] Kumar, S., Narasimhan, M.S., and Ramanathan, A., Infinite Grassmannians and moduli spaces of G-bundles, Math. Annalen 300, 41–75 (1994).MathSciNetCrossRefMATHGoogle Scholar
  24. [L] Lang, S., Introduction to Arakelov Theory, Berlin-Heidelberg-New York, Springer, 1988.CrossRefMATHGoogle Scholar
  25. [Le] Le Potier, J., Fibrés Vectoriels sur les Courbes Algébriques, Cours de DEA, Université Paris 7, 1991.Google Scholar
  26. [M] Mathieu, O., Formules de caractères pour les algèbres de Kac-Moody générales, Astérisque 159–160, 1–267, (1988).Google Scholar
  27. [Mum] Mumford, D., The Red Book of Varieties and Schemes, Springer Lecture Notes in Math., no. 1358, Berlin-Heidelberg-New York, 1988.Google Scholar
  28. [NRa] Narasimhan, M.S. and Ramadas, T.R., Factorisation of generalised theta functions. I, Invent. Math. 114, 565–623, (1993).MathSciNetCrossRefMATHGoogle Scholar
  29. [NR] Narasimhan, M.S. and Ramanan, S., Moduli of vector bundles on a compact Riemann surface, Ann. of Math. 89, 14–51, (1969).MathSciNetCrossRefMATHGoogle Scholar
  30. [NS] Narasimhan, M.S. and Seshadri, C.S., Stable and unitary vector bundles on a compact Riemann surface, Ann. of Math. 82, 540–567, (1965).MathSciNetCrossRefMATHGoogle Scholar
  31. [PS] Pressley, A. and Segal, G., Loop Groups, Oxford Science Publications, Clarendon Press, Oxford, 1986.MATHGoogle Scholar
  32. [Q] Quillen, D., Determinants of Cauchy-Riemann operators over a Riemann surface, Funct. Anal. Appl. 19, 31–34, (1985).MathSciNetCrossRefMATHGoogle Scholar
  33. [Ra] Raghunathan, M. S., Principal bundles on affine space, In: C.P. Ramanujam—A Tribute, T.I.F.R. Studies in Math., no. 8, Oxford University Press, pp. 187–206, 1978.Google Scholar
  34. [RR] Ramanan, S. and Ramanathan, A., Some remarks on the instability flag, Tohoku Math. J. 36, 269–291, (1984).MathSciNetCrossRefMATHGoogle Scholar
  35. [R1] Ramanathan, A., Stable principal bundles on a compact Riemann surface-Construction of moduli space, Thesis, University of Bombay, 1976.Google Scholar
  36. [R2] Ramanathan, A., Stable principal bundles on a compact Riemann surface, Math. Ann. 213, 129–152, (1975).MathSciNetCrossRefMATHGoogle Scholar
  37. [R3] Ramanathan, A., Deformations of principal bundles on the projective line, Invent. Math. 71, 165–191, (1983).MathSciNetCrossRefMATHGoogle Scholar
  38. [Sa] Šafarevič, I.R., On some infinite-dimensional groups. II, Math. USSR Izvestija 18, 185–194, (1982).CrossRefGoogle Scholar
  39. [Se1] Serre, J.P., Espaces fibrés algébriques, In: Anneaux de Chow et applications, Séminaire C. Chevalley, 1958.Google Scholar
  40. [Se2] Serre, J.P., Cohomologie Galoisienne, Springer Lecture Notes in Math., vol. 5, Berlin-Heidelberg-New York, 1964.Google Scholar
  41. [Sl] Slodowy, P., On the geometry of Schubert varieties attached to Kac-Moody Lie algebras, In: Can. Math. Soc. Conf. Proc. on ‘Algebraic Geometry’ (Vancouver), vol. 6, pp. 405–442, 1984.Google Scholar
  42. [TUY] Tsuchiya, A., Ueno, K. and Yamada, Y., Conformal field theory on universal family of stable curves with gauge symmetries, Adv. Stud. Pure Math. 19, 459–565, (1989).MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Shrawan Kumar
    • 1
  1. 1.Department of MathematicsUniversity of North CarolinaChapel HillUSA

Personalised recommendations