Toward a conjecture of Pappas and Rapoport on a scheme attached to the symplectic group

Abstract

We consider a closed subscheme V of the scheme of n × n skew-symmetric matrices. Over a field F of characteristic not 2, V is isomorphic to the scheme appearing in Pappas-Rapoport conjecture on local models of unitary Shimura varieties. With the additional assumption on we prove the coordinate ring of V has a basis consisting of products of pfaffians labeled by King’s symplectic standard tableaux with no odd-sized rows. When n is divisible by 4, the basis can be used to show that the coordinate ring of V is an integral domain, and this proves a special case of Pappas-Rapoport conjecture.