A new Littlewood-Richardson rule for Schur P-functions

A new description of shifted Littlewood-Richardson coefficients is given in terms of semistandard decomposition tableaux which were recently introduced by L. Serrano. We also show that the set of semistandard decomposition tableaux is invariant under the action of Lascoux-Schützenberger involution,...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2013-02, Vol.365 (2), p.939-972
Main Author: CHO, SOOJIN
Format: Article
Language:English
Online Access:Get full text
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Summary:A new description of shifted Littlewood-Richardson coefficients is given in terms of semistandard decomposition tableaux which were recently introduced by L. Serrano. We also show that the set of semistandard decomposition tableaux is invariant under the action of Lascoux-Schützenberger involution, providing a combinatorial proof of the symmetry of Schur P-functions, proving the falsity of the conjecture. Many combinatorial properties of semistandard decomposition tableaux are also shown.
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-2012-05653-4