The Poset of k-Shapes and Branching Rules for k-Schur Functions

ISBN-13: 9780821872949 / Angielski

Thomas Lam

Opis

The authors 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-cores and k 1-cores. The authors define a symmetric function for each k-shape, and show that they expand positively in terms of dual k-Schur functions. They obtain an explicit combinatorial description of the expansion of an ungraded k-Schur function into k 1-Schur functions. As a corollary, they give a formula for the Schur expansion of an ungraded k-Schur function.

Spis treści

Table of Contents <ul><li>Introduction</li><li> The poset of $k$-shapes </li><li>Equivalence of paths in the poset of $k$-shapes </li><li>Strips and tableaux for $k$-shapes </li><li>Pushout of strips and row moves </li><li>Pushout of strips and column moves </li><li>Pushout sequences </li><li>Pushouts of equivalent paths are equivalent </li><li>Pullbacks </li><li>Appendix A. </li><li>Tables of branching polynomials </li><li>Bibliography </li></ul>