Inventiones mathematicae

, Volume 116, Issue 1, pp 329–346

A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras

  • Peter Littelmann
Article

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References

  1. 1.
    Humphreys, J.E.: Introduction to Lie Algebras and Representation Theory. Berlin Heidelberg New York: Springer 1968Google Scholar
  2. 2.
    Kac, V.: Infinite-dimensional Lie-algebras. Cambridge: Cambridge University Press 1985Google Scholar
  3. 3.
    Kashiwara, M.: Crystalizing theq-analogue of Universal Enveloping algebras. Commun. Math. Phys.133, 249–260 (1990)Google Scholar
  4. 4.
    Kashiwara, M.: Crystalizing theq-analogue of Universal Enveloping algebras, Preprint, Res. Inst. Math. Sci.133 (1990)Google Scholar
  5. 5.
    Kashiwara, M.: Crystal base and Littelmann's refined Demazure character formula. Preprint. Res. Inst. Math. Sci.133 (1992)Google Scholar
  6. 6.
    Klimyk, A.U.: Decomposition of a tensor product of irreducible representations of a semi-simple Lie algebra into a direct sum of irreducible representations. Transl., II. Ser., Am. Math. Soc.76, 63–73 (1968)Google Scholar
  7. 7.
    Kumar, S.: Proof of the Parthasarathy-Ranga-Rao-Varadarajan Conjecture. Invent. Math.93, 117–130 (1988)Google Scholar
  8. 8.
    Kumar, S.: Demazure character formula in arbitrary Kac-Moody setting. Invent. Math.89, 395–423 (1987)Google Scholar
  9. 9.
    Lakshmibai, V., Seshadri, C.S.: Standard monomial theory. In: Proceedings of the Hyderabad Conference on Algebraic Groups, pp. 279–323. Madras: Manoj Prakashan 1991Google Scholar
  10. 10.
    Lakshmibai, V., Seshadri, C.S.: Geometry ofG/P V. J. Algebra100, 462–557 (1986).Google Scholar
  11. 11.
    Littelmann, P.: A generalization of the Littlewood-Richardson rule. J. Algebra130, 328–368 (1990)Google Scholar
  12. 12.
    Littelmann, P.: Young tableaux and crystal bases. (Preprint); J. Algebra (to appear, 1992)Google Scholar
  13. 13.
    Mathieu, O.: Construction d'un groupe de Kac-Moody et applications. Compos. Math.69, 37–60 (1989)Google Scholar
  14. 14.
    Mathieu, O.: Formules de caractères pour les algèbres de Kac-Moody générales. Astérisque159–160 (1988)Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Peter Littelmann
    • 1
  1. 1.Mathematisches Institut der Universität BaselBaselSwitzerland

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