Involve: A Journal of Mathematics
- Volume 9, Number 3 (2016), 437-451.
Quantum Schubert polynomials for the $G_2$ flag manifold
We study some combinatorial objects related to the flag manifold of Lie type . Using the moment graph of , we calculate all the curve neighborhoods for Schubert classes. We use this calculation to investigate the ordinary and quantum cohomology rings of . As an application, we obtain positive Schubert polynomials for the cohomology ring of and we find quantum Schubert polynomials which represent Schubert classes in the quantum cohomology ring of .
Involve, Volume 9, Number 3 (2016), 437-451.
Received: 18 February 2015
Accepted: 29 May 2015
First available in Project Euclid: 22 November 2017
Permanent link to this document
Digital Object Identifier
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]
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