论文标题
sp $ _ {2n}（k）$上的一类理查森和标志品种的定义方程式
The defining equations of a class of Richardson and flag varieties on Sp$_{2n}(k)$
论文作者
论文摘要
本文旨在将Richardson品种集中在符号群体上，尤其是其组合表征和定义方程式。舒伯特的品种和相反的舒伯特品种在对广义旗品种的研究中具有深远的意义，这些品种不仅是代数几何形状的研究对象，而且是代表理论中的对象。更一般的研究对象是Richardson品种，它是通过Schubert品种和相反的Schubert品种获得的。 Richardson在Grassmannian及其组合表征上的结构是众所周知的，并且在符号群体的商方面也有类似的方法。在本文的第一部分中，我们计算符号组动作的轨道，然后严格地提供了一种方法来通过使用线性空间的嵌套子空间序列（即标志）来描述相应的商。同时，旗帜用于描述舒伯特综合体的Schubert品种和Richardson综艺。 Sp_ {2n}（k）/p_d的标志品种可以看作是Grassmannian的封闭次级。使用标准的单体理论，我们在格拉曼尼亚人的均匀坐标环中获得其理想的发生器，即其定义方程。此外，我们证明了C型标准单元在Symbletectic组标志品种上的几种属性。也给出了sp_ {2n}（k）/p_d上理查森品种的方程式。
This paper aims to focus on Richardson varieties on symplectic groups, especially their combinatorial characterization and defining equations. Schubert varieties and opposite Schubert varieties have profound significance in the study of generalized flag varieties which are not only research objects in algebraic geometry but also ones in representation theory. A more general research object is Richardson variety, which is obtained by the intersection of a Schubert variety and an opposite Schubert variety. The structure of Richardson variety on Grassmannian and its combinatorial characterization are well known, and there are also similar method on quotients of symplectic groups. In the first part of this paper, we calculate the orbit of the symplectic group action, and then rigorously give a method to describe the corresponding quotient by using the nesting subspace sequence of the linear space, i.e. flags. At the same time, the flag is used to describe the Schubert variety and Richardson variety on quotient of symplectic group. The flag varieties of Sp_{2n}(k)/P_d can be viewed as closed subvarieties of Grassmannian. Using the standard monomial theory, we obtain the generators of its ideal, i.e. its defining equations, in homogeneous coordinate ring of Grassmannian. Furthermore, we prove several properties of the type C standard monomial on the symplectic group flag variety. Defining equations of Richardson varieties on Sp_{2n}(k)/P_d are given as well.
