Geodesic
Flag Gromov-Witten invariants via crystals
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) (2014).

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We apply ideas from crystal theory to affine Schubert calculus and flag Gromov-Witten invariants. By defining operators on certain decompositions of elements in the type-$A$ affine Weyl group, we produce a crystal reflecting the internal structure of Specht modules associated to permutation diagrams. We show how this crystal framework can be applied to study the product of a Schur function with a $k$-Schur function. Consequently, we prove that a subclass of 3-point Gromov-Witten invariants of complete flag varieties for $\mathbb{C}^n$ enumerate the highest weight elements under these operators. 
@article{DMTCS_2014_special_265_a42,
     author = {Morse, Jennifer and Schilling, Anne},
     title = {Flag {Gromov-Witten} invariants via crystals},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)},
     year = {2014},
     doi = {10.46298/dmtcs.2417},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2417/}
}
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%A Morse, Jennifer
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%J Discrete mathematics & theoretical computer science
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%I mathdoc
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Morse, Jennifer; Schilling, Anne. Flag Gromov-Witten invariants via crystals. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) (2014). doi : 10.46298/dmtcs.2417. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2417/

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