论文标题
古典谎言超级甲虫
The Nilpotent Cone for Classical Lie Superalgebras
论文作者
论文摘要
在本文中，作者引入了nilpotent锥的类似物，$ {\ mathcal n} $，用于经典的谎言superalgebra，$ {\ mathfrak g} $，它概括了nilpotent圆锥的半粘膜lie lie algebras的定义。对于经典的简单谎言superalgebra，$ {\ mathfrak g} = {\ mathfrak g} _ {\ bar {0}} \ oplus {\ mathfrak g} _ {\ bar {\ bar {\ bar {1}}} g} _ {\ bar {0}} $，显示出有限的$ g _ {\ bar {0}}} $ - orbits $ {\ mathcal n} $。后来，作者证明了duflo-serganova的通勤品种，$ {\ mathcal x} $，用于$ {\ mathcal n} $中的任何经典简单的lie superalgebra。因此，我们的有限性概括并扩展了Duflo-Serganova在通勤品种上的工作。在本文的末尾给出了进一步的申请。
In this paper the authors introduce an analog of the nilpotent cone, ${\mathcal N}$, for a classical Lie superalgebra, ${\mathfrak g}$, that generalizes the definition for the nilpotent cone for semisimple Lie algebras. For a classical simple Lie superalgebra, ${\mathfrak g}={\mathfrak g}_{\bar{0}}\oplus {\mathfrak g}_{\bar{1}}$ with $\text{Lie }G_{\bar{0}}={\mathfrak g}_{\bar{0}}$, it is shown that there are finitely many $G_{\bar{0}}$-orbits on ${\mathcal N}$. Later the authors prove that the Duflo-Serganova commuting variety, ${\mathcal X}$, is contained in ${\mathcal N}$ for any classical simple Lie superalgebra. Consequently, our finiteness result generalizes and extends the work of Duflo-Serganova on the commuting variety. Further applications are given at the end of the paper.
