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, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
[AM] Atiyah, M.F. and Macdonald, I.G., Introduction to Commutative Algebra, Addison-Wesley, 1969.
[BL] Beauville, A. and Laszlo, Y., Conformal blocks and generalized theta functions, Commun. Math. Phys. 164, 385–419, (1994).
[BL2] Beauville, A. and Laszlo, Y., Un lemme de descente, C.R. Acad. Sci. Paris 320, 335–340, (1995).
[B] Borel, A., Linear Algebraic Groups, W.A. Benjamin, New York, 1969.
[Bo] Bourbaki, N., Groupes et Algèbres de Lie, Chap. 4–6, Masson, Paris, 1981.
[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).
[D] Dynkin, E.B., Semisimple subalgebras of semisimple Lie algebras, Am. Math. Soc. Transl. (Ser. II) 6, 111–244, (1957).
[Fa] Faltings, G., A proof for the Verlinde formula, J. Alg. Geom. 3, 347–374, (1994).
[F] Fulton, W., Introduction to Intersection Theory in Algebraic Geometry, Reg. Conf. Ser. in Math., number 54, AMS, Providence, RI, 1984.
[G] Grothendieck, A., Éléments de géométrie algébrique IV (Seconde Partie), Publications Math. IHES 24, (1965).
[GK] Guruprasad, K. and Kumar, S., A new geometric invariant associated to the space of flat connections, Compositio Math. 73, 199–222, (1990).
[H1] Harder, G., Halbeinfache gruppenschemata über Dedekindringen, Invent. Math. 4, 165–191, (1967).
[H2] Harder, G., Halbeinfache gruppenschemata über vollständigen kurven, Invent. Math. 6, 107–149, (1968).
[Ha] Hartshorne, R., Algebraic Geometry, Berlin-Heidelberg-New York, Springer, 1977.
[Hu] Humphreys, J.E., Introduction to Lie Algebras and Representation Theory, Graduate Texts in Math., vol. 9, Berlin-Heidelberg-New York, Springer, 1972.
[Hur] Hurtubise, J.C., Holomorphic maps of a Riemann surface into a flag manifold, J. of Diff. Geom. 43, 99–118, (1996).
[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).
[K] Kac, V.G., Infinite Dimensional Lie Algebras, Third edition, Cambridge, Cambridge University Press, 1990.
[KL] Kazhdan, D. and Lusztig, G., Schubert varieties and Poincare duality, Proc. Symp. Pure Math. (A.M.S.) 36, 185–203, (1980).
[KL2] Kazhdan, D. and Lusztig, G., Tensor structures arising from affine Lie algebras, J. of A.M.S. 6, 905–947, (1993).
[Ku1] Kumar, S., Demazure character formula in arbitrary Kac-Moody setting, Invent Math. 89, 395–423, (1987).
[Ku2] Kumar, S., Normality of certain Springer fibers, (handwritten notes), 1986.
[KNR] Kumar, S., Narasimhan, M.S., and Ramanathan, A., Infinite Grassmannians and moduli spaces of G-bundles, Math. Annalen 300, 41–75 (1994).
[L] Lang, S., Introduction to Arakelov Theory, Berlin-Heidelberg-New York, Springer, 1988.
[Le] Le Potier, J., Fibrés Vectoriels sur les Courbes Algébriques, Cours de DEA, Université Paris 7, 1991.
[M] Mathieu, O., Formules de caractères pour les algèbres de Kac-Moody générales, Astérisque 159–160, 1–267, (1988).
[Mum] Mumford, D., The Red Book of Varieties and Schemes, Springer Lecture Notes in Math., no. 1358, Berlin-Heidelberg-New York, 1988.
[NRa] Narasimhan, M.S. and Ramadas, T.R., Factorisation of generalised theta functions. I, Invent. Math. 114, 565–623, (1993).
[NR] Narasimhan, M.S. and Ramanan, S., Moduli of vector bundles on a compact Riemann surface, Ann. of Math. 89, 14–51, (1969).
[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).
[PS] Pressley, A. and Segal, G., Loop Groups, Oxford Science Publications, Clarendon Press, Oxford, 1986.
[Q] Quillen, D., Determinants of Cauchy-Riemann operators over a Riemann surface, Funct. Anal. Appl. 19, 31–34, (1985).
[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.
[RR] Ramanan, S. and Ramanathan, A., Some remarks on the instability flag, Tohoku Math. J. 36, 269–291, (1984).
[R1] Ramanathan, A., Stable principal bundles on a compact Riemann surface-Construction of moduli space, Thesis, University of Bombay, 1976.
[R2] Ramanathan, A., Stable principal bundles on a compact Riemann surface, Math. Ann. 213, 129–152, (1975).
[R3] Ramanathan, A., Deformations of principal bundles on the projective line, Invent. Math. 71, 165–191, (1983).
[Sa] Šafarevič, I.R., On some infinite-dimensional groups. II, Math. USSR Izvestija 18, 185–194, (1982).
[Se1] Serre, J.P., Espaces fibrés algébriques, In: Anneaux de Chow et applications, Séminaire C. Chevalley, 1958.
[Se2] Serre, J.P., Cohomologie Galoisienne, Springer Lecture Notes in Math., vol. 5, Berlin-Heidelberg-New York, 1964.
[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.
[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).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer-Verlag
About this chapter
Cite this chapter
Kumar, S. (1997). Infinite grassmannians and moduli spaces of G-bundles. In: Narasimhan, M.S. (eds) Vector Bundles on Curves — New Directions. Lecture Notes in Mathematics, vol 1649. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094424
Download citation
DOI: https://doi.org/10.1007/BFb0094424
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62401-1
Online ISBN: 978-3-540-49701-1
eBook Packages: Springer Book Archive
