## Involve: A Journal of Mathematics

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

### Quantum Schubert polynomials for the $G_2$ flag manifold

#### 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
Accepted: 29 May 2015
First available in Project Euclid: 22 November 2017

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

#### 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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