Vol. 9, No. 3, 2016

 Recent Issues
 The Journal Cover Page Editorial Board Editors’ Addresses Editors’ Interests About the Journal Scientific Advantages Submission Guidelines Submission Form Ethics Statement Subscriptions Editorial Login Author Index Coming Soon Contacts ISSN: 1944-4184 (e-only) ISSN: 1944-4176 (print)
Quantum Schubert polynomials for the $G_2$ flag manifold

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

Vol. 9 (2016), No. 3, 437–451
Abstract

We study some combinatorial objects related to the flag manifold $X$ of Lie type ${G}_{2}$. 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 $X$.

Keywords
quantum cohomology, Schubert polynomial, $G_2$ flag manifold
Mathematical Subject Classification 2010
Primary: 14N15
Secondary: 14M15, 14N35, 05E15