Positivity determines the quantum cohomology of the odd symplectic Grassmannian of lines

Let IG:=IG(2,2n+1) denote the odd symplectic Grassmannian of lines which is a horospherical variety of Picard rank 1. The quantum cohomology ring QH*(IG) has negative structure constants. For n≥3, we give a positivity condition that implies the quantum cohomology ring QH*(IG) is the only quantum deformation of the cohomology ring H*(IG) up to the scaling of the quantum parameter. This is a modification of a conjecture by Fulton.