Reduced arc schemes for Veronese embeddings and global Demazure modules
Reduced arc schemes for Veronese embeddings and global Demazure modules
复制标题
Veronese 嵌入和全局 Demazure 模块的简化弧方案
DOI：
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发表时间：
2019
影响因子：
1.6
通讯作者：
E. Feigin
中科院分区：
文献类型：
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作者：
Ilya Dumanski;E. Feigin
本文研究ADE型单李群的旗簇的Veronese嵌入的投影弧格式。圆弧格式没有约化，我们考虑相应约化格式的齐次坐标环。我们证明了齐次坐标环的每个分次分量都是当前代数的上循环模，并且作用于对称多项式代数。我们证明了多项式代数的作用是自由的，并且分次分量在特殊点处的局部化同构于仿射Demazure模，其水平是Veronese嵌入的程度。在A_1型中，我们给出了Veronese曲线的约化弧格式结构的生成元的精确列表。在一般类型中，我们引入了整体高阶Demazure模的概念，并利用这些模确定了齐次坐标环的分次分量。
We consider the projective arc schemes of the Veronese embeddings of the flag varieties for simple Lie groups of type ADE. The arc schemes are not reduced and we consider the homogeneous coordinate rings of the corresponding reduced schemes. We show that each graded component of a homogeneous coordinate ring is a cocyclic module of the current algebra and is acted upon by the algebra of symmetric polynomials. We show that the action of the polynomial algebra is free and that the localization at the special point of a graded component is isomorphic to an affine Demazure module whose level is the degree of the Veronese embedding. In type $A_1$ we give the precise list of generators of the reduced arc scheme structure of the Veronese curves. In general type we introduce the notion of the global higher level Demazure modules and identify the graded components of the homogeneous coordinate rings with these modules.