The Drinfel’d Lagrangian Grassmannian compactifies the space of algebraic maps of fixed degree from the projective line into the Lagrangian Grassmannian. It has a natural projective embedding arising from the highest weight embedding of the ordinary Lagrangian Grassmannian, and one may study its defining ideal in this embedding.The Drinfel’d Lagrangian Grassmannian is singular. However, a concrete description of generators for the defining ideal of the Schubert subvarieties of the Drinfel’d Lagrangian Grassmannian would implythat the singularities are modest. I prove that the defining ideal of any Schubert subvariety is generated by polynomials which give a straightening law on an ordered set. Using this fact, I show that any such subvariety is Cohen-Macaulay and Koszul. These results represent a partial extension of standard monomial theory to the Drinfel’d Lagrangian Grassmannian.

The Drinfel’d Lagrangian Grassmannian compactifies the space of algebraic maps of fixed degree from the projective line into the Lagrangian Grassmannian. It has a natural projective embedding arising from the highest weight embedding of the ordinary Lagrangian Grassmannian, and one may study its defining ideal in this embedding.The Drinfel’d Lagrangian Grassmannian is singular. However, a concrete description of generators for the defining ideal of the Schubert subvarieties of the Drinfel’d Lagrangian Grassmannian would implythat the singularities are modest. I prove that the defining ideal of any Schubert subvariety is generated by polynomials which give a straightening law on an ordered set. Using this fact, I show that any such subvariety is Cohen-Macaulay and Koszul. These results represent a partial extension of standard monomial theory to the Drinfel’d Lagrangian Grassmannian.