轨道的关联类和层次
The incidence class and the hierarchy of orbits
摘要：
R. Rimányi将两个奇点X和Y的关联类定义为$[X]|_Y$，X到Y的Thom多项式的限制。他解释说（在温和的条件下）当且仅当Y在X的闭包中时，发生率不为零。推广这一概念，我们定义了一个表示的两个轨道X和Y的关联类。我们给出了Y具有关联类$[X]|_Y$不为零的充分条件（正性）当且仅当Y对于任何其它轨道X都在X的闭包中.我们表明，对于许多有趣的情况下，例如，Dynkin型正性的双线性表示持有所有的轨道。换句话说，在这些情况下，关联类完全决定了轨道的层次。我们还研究了奇点的情况下，积极性不持有所有的轨道。
英文摘要：
R. Rimányi defined the incidence class of two singularities X and Y as $[X]|_Y$, the restriction of the Thom polynomial of X to Y. He conjectured that (under mild conditions) the incidence is not zero if and only if Y is in the closure of X. Generalizing this notion we define the incidence class of two orbits X and Y of a representation. We give a sufficient condition (positivity) for Y to have the property that the incidence class $[X]|_Y$ is not zero if and only if Y is in the closure of X for any other orbit X. We show that for many interesting cases, e.g. the quiver representations of Dynkin type positivity holds for all orbits. In other words in these cases the incidence classes completely determine the hierarchy of the orbits. We also study the case of singularities where positivity doesn't hold for all orbits.
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