Quantum cohomology of the odd symplectic Grassmannian of lines

TL;DR

This paper computes the classical and quantum cohomology of odd symplectic Grassmannians of lines, revealing semi-simplicity and confirming Dubrovin's conjecture despite their non-homogeneous nature.

Contribution

It provides explicit Pieri and Giambelli formulas for odd symplectic Grassmannians and demonstrates their quantum cohomology is semi-simple, extending known results to a new class.

Findings

Quantum cohomology is semi-simple.

Pieri and Giambelli formulas are similar to the symplectic case.

Dubrovin's conjecture is verified for these varieties.

Abstract

Odd symplectic Grassmannians are a generalization of symplectic Grassmannians to odd-dimensional spaces. Here we compute the classical and quantum cohomology of the odd symplectic Grassmannian of lines. Although these varieties are non homogeneous, we obtain Pieri and Giambelli formulas that are very similar to the symplectic case. We notice that their quantum cohomology is semi-simple, which enables us to check Dubrovin's conjecture for this case.