Growth diagrams for the Schubert multiplication

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:117

Article

Lenart, Cristian

关键词: Schubert calculus;    Flag variety;    Littlewood-Richardson rule;    Plactic relation;    Jeu de taquin;    Growth diagram;    k-Bruhat order;   

DOI  :  10.1016/j.jcta.2010.02.004

来源: Elsevier

【 摘 要 】

We present a partial generalization of the classical Littlewood-Richardson rule (in its version based on Schutzenberger's jeu de taquin) to Schubert calculus on flag varieties. More precisely, we describe certain structure constants expressing the product of a Schubert and a Schur polynomial. We use a generalization of Fomin's growth diagrams (for chains in Young's lattice of partitions) to chains of permutations in the so-called k-Bruhat order. Our work is based on the recent thesis of Beligan, in which he generalizes the classical plactic structure on words to chains in certain intervals in k-Bruhat order. Potential applications of our work include the generalization of the S-3-symmetric Littlewood-Richardson rule due to Thomas and Yong, which is based on Fomin's growth diagrams. (C) 2010 Elsevier Inc. All rights reserved.

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