The Poset of [kappa]-shapes and Branching Rules for [kappa]-Schur Functions PDF Download

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The Poset of [kappa]-shapes and Branching Rules for [kappa]-Schur Functions

The Poset of [kappa]-shapes and Branching Rules for [kappa]-Schur Functions PDF Author: Thomas Lam
Publisher:
ISBN: 9780821898741
Category : Partially ordered sets
Languages : en
Pages : 101

Book Description
We give a combinatorial expansion of a Schubert homology class in the affine Grassmannian GrSLk into Schubert homology classes in GrSLk+1. This is achieved by studying the combinatorics of a new class of partitions called k-shapes, which interpolates between k k-cores and kk+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 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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