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The Poset of K-Shapes and Branching Rules for K-Schur Functions (Memoirs of the American Mathematical Society)

Discrete Mathematics

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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.

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Format: paperback
ASIN: 082187294X
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Discrete Mathematics
Domain: Amazon UK
Release Date: 30 July 2013
Listed Since: 14 February 2013

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The Poset of K-Shapes and Branching Rules for K-Schur Functions (Memoirs of the American Mathematical Society)

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