Georgia Institute of Technology College of Sciences

Positroid varieties are subvarieties of the Grassmannian that arise in the study of total positivity. Knutson, Lam, and Speyer described a certain type of Gröbner degeneration called the Hodge degeneration as projections of order complexes of intervals in the Bruhat order, but their description does not give an explicit Gröbner basis nor initial ideal. We give an explicit, combinatorial description of the Gröbner basis and initial ideal corresponding to the Hodge degeneration for an arbitrary positroid variety. As an application, we show that promotion on rectangular-shaped semistandard tableaux gives a bijection between standard monomials of a positroid variety and its cyclic shifts. This is joint work with Shiliang Gao (UIUC) and Daoji Huang (Minnesota).