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A k-tableau characterization of k-Schur functions

Luc Lapointe·Jennifer Morse
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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.

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Luc Lapointe, Jennifer Morse. 2005-05-24. A k-tableau characterization of k-Schur functions. https://arxiv.org/abs/math/0505519

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