Dubrovin's conjecture for $IG(2,6)$

TL;DR

This paper demonstrates that the big quantum cohomology of the symplectic isotropic Grassmannian IG(2,6) is generically semisimple, supporting Dubrovin's conjecture and highlighting the importance of considering big quantum cohomology.

Contribution

It provides the first example where the big quantum cohomology is semisimple while the small is not, confirming a case of Dubrovin's conjecture.

Findings

Big quantum cohomology of IG(2,6) is generically semisimple.

Small quantum cohomology of IG(2,6) is non-semisimple.

Supports Dubrovin's conjecture in this context.

Abstract

We show that the big quantum cohomology of the symplectic isotropic Grassmanian $IG(2,6)$ is generically semisimple, whereas its small quantum cohomology is known to be non-semisimple. This gives yet another case where Dubrovin's conjecture holds and stresses the need to consider the big quantum cohomology in its formulation.