论文标题
朝着与符号组相关的方案上的Pappas和Rapoport的猜想
Towards a conjecture of Pappas and Rapoport on a scheme attached to the symplectic group
论文作者
论文摘要
令n = 2R为一个整数。我们考虑了n-b n偏度对称矩阵的封闭式v，在该方案上，s s sp（n）的自然作用。在不等于2的特征的场上，方案V与Pappas和Rapoport在统一Shimura品种的局部模型中出现的方案同构。使用其他假设char f = 0或char f> r，我们证明V的坐标环具有由King的Symbletic Standard Tableaux标记的Pfaffians的基础组成，没有奇数尺寸的行。当n是4的倍数时，可以使用基础来证明V的坐标环是一个整体域，这证明了Pappas和Rapoport的猜想的特殊情况。
Let n = 2r be an even integer. We consider a closed subscheme V of the scheme of n-by-n skew-symmetric matrices, on which there is a natural action of the symplectic group Sp(n). Over a field F of characteristic not equal to 2, the scheme V is isomorphic to the scheme appearing in a conjecture by Pappas and Rapoport on local models of unitary Shimura varieties. With the additional assumption char F = 0 or char F > r, we prove the coordinate ring of V has a basis consisting of products of pfaffians labelled by King's symplectic standard tableaux with no odd-sized rows. When n is a multiple of 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 the conjecture by Pappas and Rapoport.
