Conjecture $\mathcal{O}$ holds for the odd symplectic Grassmannian

Abstract

Let $\mathrm{IG}(k,2n+1)$ be the odd-symplectic Grassmannian. Property $\mathcal{O}$, introduced by Galkin, Golyshev and Iritani for arbitrary complex, Fano manifolds $X$, is a statement about the eigenvalues of the linear operator obtained by the quantum multiplication by the anticanonical class of $X$. We prove that property $\mathcal{O}$ holds in the case when $X=\mathrm{IG}(k,2n+1)$ is an odd-symplectic Grassmannian. The proof uses the combinatorics of the recently found quantum Chevalley formula for $\mathrm{IG}(k,2n+1)$, together with the Perron-Frobenius theory of nonnegative matrices.

9 pages

References in corpus (5)

• Geometry of horospherical varieties of Picard rank one
• An analogue of Dubrovin's conjecture
• Gamma conjecture via mirror symmetry
• Gamma conjecture I for del Pezzo surfaces
• The moment graph for Bott-Samelson varieties and applications to quantum cohomology

Cited by in corpus (1)

• Geometry of horospherical varieties of Picard rank one