A k-tableau characterization of k-Schur functions

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.