On the Conjecture $\mathcal{O}$ of GGI for $G/P$

Abstract

In this paper, we show that general homogeneous manifolds $G/P$ satisfy Conjecture $\mathcal{O}$ of Galkin, Golyshev and Iritani which `underlies' Gamma conjectures I and II of them. Our main tools are the quantum Chevalley formula for $G/P$ and a theory on nonnegative matrices including Perron-Frobenius theorem.

arXiv comment16 pages; minor corrections; to appear in Advances in Math

References in corpus (2)

• Geometry and analytic theory of Frobenius manifolds
• Quantum cohomology and the Satake isomorphism