论文标题
具有编纂的轨道的品种上的矢量束
Equivariant Vector Bundles on Varieties with Codimension-one Orbits
论文作者
论文摘要
让$ g $为代数组，让$ x $成为一个光滑的$ g $ - 带有两个轨道的变化：开放轨道和一个封闭的consimension $ 1 $。在轻度的技术假设下，我们对$ g $ equivariant vector Bundles的类别进行代数描述。我们在特殊情况下推断出更简单的分类，即通常是本地系统的载体束。我们将结果应用于对半圣母谎言群体的可接受代表的研究。我们的主要结果给出了对单位表示相关周期的新约束。
Let $G$ be an algebraic group and let $X$ be a smooth $G$-variety with two orbits: an open orbit and a a closed orbit of codimension $1$. We give an algebraic description of the category of $G$-equivariant vector bundles on $X$ under a mild technical hypothesis. We deduce simpler classifications in the special cases of line bundles and vector bundles which are generically local systems. We apply our results to the study of admissible representations of semisimple Lie groups. Our main result gives a new set of constraints on the associated cycles of unipotent representations.
