Browsing by Author "Mihalcea, Leonardo C."
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- Quantum K Whitney relations for partial flag varietiesGu, Wei; Mihalcea, Leonardo C.; Sharpe, Eric; Xu, Weihong; Zhang, Hao; Zou, Hao (2023-10-05)In a recent paper, we stated conjectural presentations for the equivariant quantum K ring of partial flag varieties, motivated by physics considerations. In this companion paper, we analyze these presentations mathematically. We prove that if the conjectured relations hold, then they must form a complete set of relations. Our main result is a proof of the conjectured presentation in the case of the incidence varieties. We also show that if a quantum K divisor axiom holds (as conjectured by Buch and Mihalcea), then the conjectured presentation also holds for the complete flag variety.
- Quantum Schubert polynomials for the G2 flag manifoldElliott, Rachel; Lewers, Mark E.; Mihalcea, Leonardo C. (2016)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 b. 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.