Involve: A Journal of Mathematics

  • Involve
  • Volume 9, Number 3 (2016), 437-451.

Quantum Schubert polynomials for the $G_2$ flag manifold

Rachel E. Elliott, Mark E. Lewers, and Leonardo C. Mihalcea

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We study some combinatorial objects related to the flag manifold X of Lie type G2. Using the moment graph of X, we calculate all the curve neighborhoods for Schubert classes. We use this calculation to investigate the ordinary and quantum cohomology rings of X. As an application, we obtain positive Schubert polynomials for the cohomology ring of X and we find quantum Schubert polynomials which represent Schubert classes in the quantum cohomology ring of X.

Article information

Involve, Volume 9, Number 3 (2016), 437-451.

Received: 18 February 2015
Accepted: 29 May 2015
First available in Project Euclid: 22 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14N15: Classical problems, Schubert calculus
Secondary: 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35] 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45] 05E15: Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80]

quantum cohomology Schubert polynomial $G_2$ flag manifold


Elliott, Rachel E.; Lewers, Mark E.; Mihalcea, Leonardo C. Quantum Schubert polynomials for the $G_2$ flag manifold. Involve 9 (2016), no. 3, 437--451. doi:10.2140/involve.2016.9.437.

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