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.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-1550 |
| Date | 15 May 2009 |
| Creators | Ruffo, James Vincent |
| Contributors | Sottile, Frank |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | electronic, application/pdf, born digital |
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