# Quantum multiplication operators for Lagrangian and orthogonal Grassmannians

## TL;DR

This paper analyzes quantum multiplication operators on the quantum cohomology rings of Lagrangian and orthogonal Grassmannians, providing explicit eigenvector and eigenvalue descriptions, and confirming a key conjecture for these manifolds.

## Contribution

It offers an explicit description of eigenvectors and eigenvalues for quantum multiplication operators on these Grassmannians, confirming Conjecture O.

## Key findings

- Conjecture O holds for these manifolds.
- Explicit eigenvector and eigenvalue descriptions provided.
- Analysis advances understanding of quantum cohomology in these geometries.

## Abstract

In this article, we make a close analysis on quantum multiplication operators on the quantum cohomology rings of Lagrangian and orthogonal Grassmannians, and give an explicit description on all simultaneous eigenvectors and the corresponding eigenvalues for these operators. As a result, we show that Conjecture $\mathcal{O}$ of Galkin, Golyshev and Iritani holds for these manifolds.