Geodesic
Young straightening in a quotient $S\sb n$-module
Journal of Algebraic Combinatorics, Tome 2 (1993) no. 1, pp. 5-23.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We describe a straightening algorithm for the action of $S _{n}$ on a certain graded ring $R _{ m} R_\mu $. The ring $R _{ m} R_\mu $appears in the work of C. de Concini and C. Procesi [2] and T. Tanisaki [8], and more recently in the work of A. Garsia and C. Procesi [4]. This ring is a graded version of the permutation representation resulting from the action of $S _{n}$ on the left cosets of a Young subgroup. As a corollary of our straightening algorithm we obtain a combinatorial proof of the fact that the top degree component of $R _{ m} R_\mu $affords the irreducible representation of $S _{n}$ indexed by $mgr$.
Keywords: graded permutation representation, straightening algorithm, Young's natural representation, symmetric group 
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     title = {Young straightening in a quotient $S\sb n$-module},
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Barcelo, Hélène. Young straightening in a quotient $S\sb n$-module. Journal of Algebraic Combinatorics, Tome 2 (1993) no. 1, pp. 5-23. http://geodesic.mathdoc.fr/item/JAC_1993__2_1_a5/