On the quantum parameter in the quantum cohomology of a family of odd symplectic partial flag varieties

TL;DR

This paper investigates the structure of the quantum cohomology ring of a specific family of odd symplectic partial flag varieties, revealing the repeated appearance of a particular quantum parameter product in quantum products.

Contribution

It demonstrates the explicit occurrence and multiplicity of the quantum parameter product in the quantum cohomology of odd symplectic partial flag varieties.

Findings

The product $q_1q_2\cdots q_m$ appears $m$ times in certain quantum products.

The structure of the quantum cohomology ring is explicitly characterized for the family of varieties.

The results provide new insights into the quantum parameters in symplectic geometry.

Abstract

We will consider a particular family of odd symplectic partial flag varieties denoted by $\mbox{IF}$. In the quantum cohomology ring $\mbox{QH}^*(\mbox{IF})$, we will show that $q_1q_2\cdots q_m$ appears $m$ times in the quantum product $\tau_{Div_i} \star \tau_{id}$ when expressed as a sum in terms of the Schubert basis.