Letters in Mathematical Physics

, Volume 10, Issue 2, pp 111–124

Schubert polynomials and the Littlewood-Richardson rule

  • Alain Lascoux
  • Marcel-Paul Schützenberger
Article

DOI: 10.1007/BF00398147

Cite this article as:
Lascoux, A. & Schützenberger, MP. Lett Math Phys (1985) 10: 111. doi:10.1007/BF00398147

Abstract

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).

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