The Poset of K-Shapes and Branching Rules for K-Schur Functions (Memoirs of the American Mathematical Society)
Author： Thomas Lam;Luc Lapointe;Jennifer Morse
Publisher： American Mathematical Society
Publication year： 2013
E-ISBN: 9780821898741
P-ISBN(Paperback): 9780821872949
P-ISBN(Hardback): 9780821872949
Subject： O153.1 partially ordered sets and lattices
Keyword： Discrete Mathematics and Combinatorics
Language： ENG
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The Poset of K-Shapes and Branching Rules for K-Schur Functions (Memoirs of the American Mathematical Society)
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.