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

TL;DR

This paper proves that all general homogeneous manifolds of the form G/P satisfy Conjecture O, supporting the broader Gamma conjectures, using quantum Chevalley formulas and Perron-Frobenius theory.

Contribution

It establishes the validity of Conjecture O for G/P manifolds, linking quantum cohomology with nonnegative matrix theory.

Findings

G/P manifolds satisfy Conjecture O

Supports Gamma conjectures I and II

Uses quantum Chevalley formula and Perron-Frobenius theorem

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.