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arXiv · 1007.5334

k-shape poset and branching of k-Schur functions

Thomas Lam·Luc Lapointe·Jennifer Morse·Mark Shimozono
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Abstract

We give a combinatorial expansion of a Schubert homology class in the affine Grassmannian Gr_{SL_k} into Schubert homology classes in Gr_{SL_{k+1}}. This is achieved by studying the combinatorics of a new class of partitions called k-shapes, which interpolates between k-cores and k+1-cores. We define a symmetric function for each k-shape, and show that they expand positively in terms of dual k-Schur functions. We obtain an explicit combinatorial description of the expansion of an ungraded k-Schur function into k+1-Schur functions. As a corollary, we give a formula for the Schur expansion of an ungraded k-Schur function.

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Thomas Lam, Luc Lapointe, Jennifer Morse, Mark Shimozono. 2010-07-29. k-shape poset and branching of k-Schur functions. https://arxiv.org/abs/1007.5334

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