Jennifer Morse ; Anne Schilling - Flag Gromov-Witten invariants via crystals

dmtcs:2417 - Discrete Mathematics & Theoretical Computer Science, January 1, 2014, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) - https://doi.org/10.46298/dmtcs.2417
Flag Gromov-Witten invariants via crystals

Authors: Jennifer Morse 1,2; Anne Schilling 3

  • 1 Drexel University
  • 2 Department of mathematics [Philadelphie]
  • 3 Department of Mathematics [Univ California Davis]

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.


Volume: DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Section: Proceedings
Published on: January 1, 2014
Imported on: November 21, 2016
Keywords: flag Gromov-Witten invariants,Littlewood–Richardson coefficients,crystal graphs,Specht modules,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]
Funding:
    Source : OpenAIRE Graph
  • Combinatorics in algebra, geometry, and physics; Funder: National Science Foundation; Code: 1301695
  • Affine Combinatorics; Funder: National Science Foundation; Code: 1001256
  • Combinatorics of affine Schubert calculus, K-theory, and Macdonald polynomials; Funder: National Science Foundation; Code: 1001898
  • Collaborative Research: SI2-SSE: Sage-Combinat: Developing and Sharing Open Source Software for Algebraic Combinatorics; Funder: National Science Foundation; Code: 1147247

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