Percentage-Avoiding, Northwest Shapes and Peelable Tableaux

Victor Reiner, Mark Shimozono

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21 Scopus citations

Abstract

We prove three results for Specht and Schur modules associated tonorthwest shapesand the more general class of%-avoiding shapes. The first result (conjectured for northwest shapes in by the authors) is a generalization the Littlewood-Richardson rule, giving an explicit combinatorial description for the multiplicities of irreducibles in the Specht and Schur modules of a %-avoiding shapeD, in terms ofD-peelable tableaux. The second result gives three involutions on the set of peelable tableaux which exhibit the symmetries of these multiplicities corresponding to three natural involutive operations on the set of %-avoiding shapes. The third result gives branching rules for the Specht and Schur modules of northwest shapes. The proofs are all combinatorial, with the exception of a key step in the first result, which requires results of Magyar on configuration varieties and characters of flagged Schur modules.

Original languageEnglish (US)
Pages (from-to)1-73
Number of pages73
JournalJournal of Combinatorial Theory. Series A
Volume82
Issue number1
DOIs
StatePublished - Apr 1998

Bibliographical note

Funding Information:
* Supported by NSF Postdoctoral Research Fellowship DMS-9206371. -Supported by NSF Postdoctoral Research Fellowship DMS-9407639.

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