A k-tableau characterization of k-Schur functions

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Aug 2007Embargo end date: 01 Jan 2005 Chile English Publisher:Elsevier BVJournal:Advances in Mathematics, volume 213, pages 183-204 (issn: 0001-8708,

Copyright policy )Funded by:NSF | Refined symmetric functio..., NSERC | unidentified, NSF | Refined symmetric functio...

Authors: Lapointe, L.; Morse, J.;

doi: 10.1016/j.aim.2006.12.005 , 10.48550/arxiv.math/0505519

arXiv: math/0505519

A k-tableau characterization of k-Schur functions

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Abstract

We study k-Schur functions characterized by k-tableaux, proving combinatorial properties such as a k-Pieri rule and a k-conjugation. This new approach relies on developing the theory of k-tableaux, and includes the introduction of a weight-permuting involution on these tableaux that generalizes the Bender-Knuth involution. This work lays the groundwork needed to prove that the set of k-Schur Littlewood-Richardson coefficients contains the 3-point Gromov-Witten invariants; structure constants for the quantum cohomology ring.

19 pages

Country

Chile

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Keywords

Mathematics(all), Symmetric functions and generalizations, Gromov-Witten invariants, Gromov–Witten invariants, tableaux, Schur functions, Tableaux, Combinatorial aspects of representation theory, 05E05, FOS: Mathematics, Infinite-dimensional Lie (super)algebras, Mathematics - Combinatorics, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), Combinatorics (math.CO), 05E10, 05E05; 05E10

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