Free Resolutions of Some Schubert Singularities in the Lagrangian Grassmannian

Abstract

In this paper we construct free resolutions of certain class of closed subvarieties of affine space of symmetric matrices (of a given size). Our class covers the symmetric determinantal varieties (i.e., determinantal varieties in the space of symmetric matrices), whose resolutions were first constructed by Józefiak-Pragacz-Weyman. Our approach follows the techniques developed in Free Resolutions of Some Schubert Singularities by Kummini-Lakshmibai-Sastry-Seshadri, and uses the geometry of Schubert varieties.

arXiv comment21 Pages, rewrote and revised some background material, updated introduction, fixed some typos, revised some proofs