论文标题
与Kostant Cascade相关的组合和几何结构
Combinatorial and geometric constructions associated with the Kostant cascade
论文作者
论文摘要
令$ \ mathfrak g $为一个复杂的简单谎言代数，$ \ mathfrak b = \ mathfrak t \ oplus \ mathfrak u^+$ a固定的borel subalgebra。令$δ^+$为与$ \ Mathfrak u^+$和$ \ Mathcal K \subsetΔ^+$ the Kostant Cascade相关的正根集。我们详细介绍了一些与$ \ Mathcal K $相关的结构以及$ \ Mathcal K $的应用。这包括Cartan subalgebra $ \ Mathfrak t $中的级联元素$ x _ {\ Mathcal k} $，以及与$ \ Mathcal K $自然相关的某些对象的属性：$ \ Mathfrak B $的Abelian Ideal of Mathfrak B $，nilpotent $ g $ g $ g $ g $ g $ g $ - g $ - g $ g $ g $ g $ a $ compriate and Antrak。
Let $\mathfrak g$ be a complex simple Lie algebra and $\mathfrak b=\mathfrak t\oplus\mathfrak u^+$ a fixed Borel subalgebra. Let $Δ^+$ be the set of positive roots associated with $\mathfrak u^+$ and $\mathcal K\subsetΔ^+$ the Kostant cascade. We elaborate on some constructions related to $\mathcal K$ and applications of $\mathcal K$. This includes the cascade element $x_{\mathcal K}$ in the Cartan subalgebra $\mathfrak t$ and properties of certain objects naturally associated with $\mathcal K$: an abelian ideal of $\mathfrak b$, a nilpotent $G$-orbit in $\mathfrak g$, and an involution of $\mathfrak g$.
