论文标题
theta代表的歧视因素
Discriminants of Theta-Representations
论文作者
论文摘要
Tevelev为复杂的简单谎言代数的判别提供了一个显式的明确公式，该公式可以定义为最小nilpotent轨道的双重性超表面的方程，或所谓的邻居品种。在本文中，我们将此公式扩展到分级谎言代数的设置，并根据与相关的复合体反射组的小Weyl组的反射表示相应的双重曲面的方程。例如，这说明了为什么Grassmannian $ G（4，8）$的代码等于$ \ Mathfrak {E} _7 $的根数。
Tevelev has given a remarkable explicit formula for the discriminant of a complex simple Lie algebra, which can be defined as the equation of the dual hypersurface of the minimal nilpotent orbit, or of the so-called adjoint variety. In this paper we extend this formula to the setting of graded Lie algebras, and express the equation of the corresponding dual hypersurfaces in terms of the reflections in the little Weyl groups, the associated complex reflection groups. This explains for example why the codegree of the Grassmannian $G(4, 8)$ is equal to the number of roots of $\mathfrak{e}_7$ .
