The Poset of k-Shapes and Branching Rules for k-Schur Functions 1

Vetenskap & teknik

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

Thomas Lam • Luc Lapointe • Jennifer Morse • Mark Shimozono

Pocket

1319:-

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101 sidor
2013

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.

Författare: Thomas Lam, Luc Lapointe, Jennifer Morse, Mark Shimozono
Format: Pocket/Paperback
ISBN: 9780821872949
Språk: Engelska
Antal sidor: 101
Utgivningsdatum: 2013-07-30
Förlag: American Mathematical Society