Letters in Mathematical Physics

, Volume 10, Issue 2–3, pp 111–124 | Cite as

Schubert polynomials and the Littlewood-Richardson rule

  • Alain Lascoux
  • Marcel-Paul Schützenberger


The decomposition of a product of two irreducible representations of a linear group Gl(N, ℂ) is explicitly given by the Littlewood-Richardson rule, which amounts to finding how many Young tableaux satisfy certain conditions. We obtain more general multiplicities by generating ‘vexillary’ permutations and by using partially symmetrical polynomials (Schubert polynomials).


Statistical Physic Group Theory Irreducible Representation Linear Group Young Tableau 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Biedenharn, L. C. and Louck, J. D., ‘Angular Momentum in Quantum Physics, Racah Wigner Algebra’, Encycl. of Maths Vols. 8, 9, Addison-Wesley, 1981.Google Scholar
  2. 2.
    LascouxA. and SchützenbergerM. P., Comptes Rendus Acad. Paris. 294, 447 (1982).Google Scholar
  3. 3.
    Lascoux, A. and Schützenberger, M. P., in Invariant Theory, Springer Lecture Notes in Maths No. 996.Google Scholar
  4. 4.
    Littlewood, D. E., The Theory of Group Characters, Oxford, 1950.Google Scholar
  5. 5.
    Macdonald, I. G., Symmetric Functions and Hall Polynomials, Oxford Maths Mono., 1979.Google Scholar
  6. 6.
    StanleyR., J. Math Phys. 21, 2321–2326 (1980).Google Scholar
  7. 7.
    StanleyR., J. Europ. Comb. 5, 359–372 (1984).Google Scholar

Copyright information

© D. Reidel Publishing Company 1985

Authors and Affiliations

  • Alain Lascoux
    • 1
  • Marcel-Paul Schützenberger
    • 1
  1. 1.LITPUER Maths Paris 7Paris Cedex 05France

Personalised recommendations