Schubert polynomials and the Littlewood-Richardson rule
- 195 Downloads
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).
KeywordsStatistical Physic Group Theory Irreducible Representation Linear Group Young Tableau
Unable to display preview. Download preview PDF.
- 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.LascouxA. and SchützenbergerM. P., Comptes Rendus Acad. Paris. 294, 447 (1982).Google Scholar
- 3.Lascoux, A. and Schützenberger, M. P., in Invariant Theory, Springer Lecture Notes in Maths No. 996.Google Scholar
- 4.Littlewood, D. E., The Theory of Group Characters, Oxford, 1950.Google Scholar
- 5.Macdonald, I. G., Symmetric Functions and Hall Polynomials, Oxford Maths Mono., 1979.Google Scholar
- 6.StanleyR., J. Math Phys. 21, 2321–2326 (1980).Google Scholar
- 7.StanleyR., J. Europ. Comb. 5, 359–372 (1984).Google Scholar