The Poset of K-Shapes and Branching Rules for K-Schur Functions
American Mathematical Society (Publisher)
Will be published approx. on 30. July 2013
Book
Paperback/Softback
101 pages
978-0-8218-7294-9 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Weight
200 gr
ISBN-13
978-0-8218-7294-9 (9780821872949)
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Schweitzer Classification
Persons
Thomas Lam, University of Michigan, Ann Arbor, MI, USA.
Luc Lapointe, Universidad de Talca, Chile.
Jennifer Morse, Drexel University, Philadelphia, PA, USA.
Mark Shimozono, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA.
Luc Lapointe, Universidad de Talca, Chile.
Jennifer Morse, Drexel University, Philadelphia, PA, USA.
Mark Shimozono, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA.
Content
Table of Contents
Introduction
The poset of $k$-shapes
Equivalence of paths in the poset of $k$-shapes
Strips and tableaux for $k$-shapes
Pushout of strips and row moves
Pushout of strips and column moves
Pushout sequences
Pushouts of equivalent paths are equivalent
Pullbacks
Appendix A.
Tables of branching polynomials
Bibliography
Introduction
The poset of $k$-shapes
Equivalence of paths in the poset of $k$-shapes
Strips and tableaux for $k$-shapes
Pushout of strips and row moves
Pushout of strips and column moves
Pushout sequences
Pushouts of equivalent paths are equivalent
Pullbacks
Appendix A.
Tables of branching polynomials
Bibliography