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A \(k\)-tableau characterization of \(k\)-Schur functions. (English) Zbl 1118.05096
Summary: 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.

MSC:
05E05 Symmetric functions and generalizations
05E10 Combinatorial aspects of representation theory
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
17B65 Infinite-dimensional Lie (super)algebras
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