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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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.involve/1511371024

Digital Object Identifier
doi:10.2140/involve.2016.9.437

Mathematical Reviews number (MathSciNet)
MR3509337

Zentralblatt MATH identifier
1365.14069

Subjects
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]

Keywords
quantum cohomology Schubert polynomial $G_2$ flag manifold

Citation

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. https://projecteuclid.org/euclid.involve/1511371024


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