论文标题
在约旦班上Vinberg的Theta-groups
On Jordan classes for Vinberg's theta-groups
论文作者
论文摘要
波波夫最近引入了约旦班级（包或分解班）的类似物，以进行theta group（g_0，v）的作用，表明它们是有限的，本地固定的，固定的，不可减少的，不可减少的g_0-orbits g_0-orbits的恒定维度分区的g_0-孔。我们在给定类中的Jordan类和G_0-Orbit在Vinberg的Little Weyl群的子组的作用方面参数，其中包括与对称案例的差异以及在Theta-Situation中产生的关键问题的几个示例和反例。
Popov has recently introduced an analogue of Jordan classes (packets, or decomposition classes) for the action of a theta-group (G_0,V), showing that they are finitely-many, locally-closed, irreducible unions of G_0-orbits of constant dimension partitioning V. We carry out a local study of their closures showing that Jordan classes are smooth and that their closure is a union of Jordan classes. We parametrize Jordan classes and G_0-orbits in a given class in terms of the action of subgroups of Vinberg's little Weyl group, and include several examples and counterexamples underlying the differences with the symmetric case and the critical issues arising in the theta-situation.
