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

Let IG : = IG (2 , 2 n + 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. [ABSTRACT FROM AUTHOR]