Landau-Ginzburg models for Homogeneous spaces

Landau-Ginzburg (LG) models have proven very useful in the study of mirror symmetry for Fano varieties. An LG model for a space X consists of a mirror space Y and a rational function on Y encoding certain enumerative data associated to X. In the particular case of homogeneous spaces, such as the Grassmannians Gr(k,n), Rietsch gave a Lie-theoretic formulation of an LG model. It is often easier to work with an LG model defined directly in terms of coordinates on Y, and in joint work with Peter Spacek, we study a Plucker coordinate construction of Rietsch's LG models for cominuscule homogeneous spaces. Along the way, we discuss several interesting connections to the geometry and representation theory of homogeneous spaces.