Quantum cohomology of the odd symplectic Grassmannian of lines

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 not homogeneous, we obtain Pieri and Giambelli formulas that are very similar to the symplectic case. We notice that their quantum cohomology is semisimple, which enables us to check Dubrovinʼs conjecture for this case.