Growth diagrams for the Schubert multiplication |
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Authors: | Cristian Lenart |
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Institution: | Department of Mathematics and Statistics, State University of New York at Albany, Albany, NY 12222, United States |
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Abstract: | We present a partial generalization of the classical Littlewood-Richardson rule (in its version based on Schützenberger'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 S3-symmetric Littlewood-Richardson rule due to Thomas and Yong, which is based on Fomin's growth diagrams. |
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Keywords: | Schubert calculus Flag variety Littlewood-Richardson rule Plactic relation Jeu de taquin Growth diagram k-Bruhat order |
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