The Poset of [kappa]-shapes and Branching Rules for [kappa]-Schur Functions
Author | : Thomas Lam |
Publisher | : |
Total Pages | : 101 |
Release | : 2013 |
ISBN-10 | : 0821898744 |
ISBN-13 | : 9780821898741 |
Rating | : 4/5 (741 Downloads) |
Download or read book The Poset of [kappa]-shapes and Branching Rules for [kappa]-Schur Functions written by Thomas Lam and published by . This book was released on 2013 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.