REVIEW 1 cited by
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
A Pl\"ucker coordinate mirror for partial flag varieties and quantum Schubert calculus
read the original abstract
We construct a Pl\"ucker coordinate superpotential $\mathcal{F}_-$ that is mirror to a partial flag variety $\mathbb{ F}\ell(n_\bullet)$. Its Jacobi ring recovers the small quantum cohomology of $\mathbb{ F}\ell(n_\bullet)$ and we prove a folklore conjecture in mirror symmetry. Namely, we show that the eigenvalues for the action of the first Chern class $c_1(\mathbb{ F}\ell(n_\bullet))$ on quantum cohomology are equal to the critical values of $\mathcal{F}_-$. We achieve this by proving new identities in quantum Schubert calculus that are inspired by our formula for $\mathcal{F}_-$ and the mirror symmetry conjecture.
Forward citations
Cited by 1 Pith paper
-
Gamma conjecture I for flag varieties
Proves Gamma conjecture I for flag varieties by showing the totally positive part of the Rietsch mirror matches the hat-Gamma class and contains the critical point for the Perron-Frobenius eigenvalue.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.