论文标题
通过量子群的共同体来实现常规功能的环
Realizing Rings of Regular Functions via the Cohomology of Quantum Groups
论文作者
论文摘要
让$ g $是一个复杂的还原组，$ p $是$ g $的抛物线亚组。在本文中，作者解决了涉及通过小型量子组的共同体实现（扭曲的）cotangent捆绑$ g/p $在全球段的$ g $模块的问题。我们的主要结果推广了Ginzburg和Kumar对小量子组的重要计算，并提供了Kumar，Lauritzen和Thomsen对量子案例和抛物线核心环境的众所周知计算的概括。作为应用程序，我们回答了一个问题（首先是Friedlander和Parshall为Frobenius内核提出的），内容涉及通过量子组的共同体来实现Richardson Orbit闭合的坐标环。将提供公式，该公式将整个部分中简单$ G $模型的多重性与大量子组的扩展组的尺寸与扩展组的尺寸相关联。
Let $G$ be a complex reductive group and $P$ be a parabolic subgroup of $G$. In this paper the authors address questions involving the realization of the $G$-module of the global sections of the (twisted) cotangent bundle over the flag variety $G/P$ via the cohomology of the small quantum group. Our main results generalize the important computation of the cohomology ring for the small quantum group by Ginzburg and Kumar, and provides a generalization of well-known calculations by Kumar, Lauritzen, and Thomsen to the quantum case and the parabolic setting. As an application we answer the question (first posed by Friedlander and Parshall for Frobenius kernels) about the realization of coordinate rings of Richardson orbit closures for complex semisimple groups via quantum group cohomology. Formulas will be provided which relate the multiplicities of simple $G$-modules in the global sections with the dimensions of extension groups over the large quantum group.
