Quiver-graded Richardson orbits
Quiver-graded Richardson orbits
复制标题
箭袋分级理查森轨道
作者：
Ögmundur Eiríksson;J. Sauter
摘要 在李理论中，抛物线群的幂零根在抛物线运算下的稠密轨道称为理查森轨道。我们定义了理查森轨道的箭袋分级版本，概括了一般线性群情况下的经典定义。我们定义了一个称为幂零箭袋代数的准遗传代数，其 Δ 滤波模的同构类对应于我们广义设置中的轨道。我们将理查森轨道的存在性转化为给定维度向量的刚性 Δ 滤波模块的存在性。我们研究了该代数的幂等重新排列，其相关的中间扩展函子可用于在某些情况下产生理查森轨道。这可以在示例中明确计算。我们还给出了不存在理查森轨道的例子。
Abstract In Lie theory, a dense orbit in the nilpotent radical of a parabolic group under the operation of the parabolic is called a Richardson orbit. We define a quiver-graded version of Richardson orbits generalizing the classical definition in the case of the general linear group. We define a quasi-hereditary algebra called the nilpotent quiver algebra whose isomorphism classes of Δ-filtered modules correspond to orbits in our generalized setting. We translate the existence of a Richardson orbit into the existence of a rigid Δ-filtered module of a given dimension vector. We study an idempotent recollement of this algebra whose associated intermediate extension functor can be used to produce Richardson orbits in some situations. This can be explicitly calculated in examples. We also give examples where no Richardson orbit exists.