论文标题
相交的顶点和广义科斯特卡锥的射线
Vertices of Intersection Polytopes and Rays of Generalized Kostka Cones
论文作者
论文摘要
令$ \ mathscr {k}（g）$为Pairs $（λ，μ）$生成的理性锥体，其中$λ$和$μ$是主要的整体权重，而$μ$是表示$v_λ$ g $的代表性$v_λ$ of $ g $。我们通过考虑相应的相交polytopes $ip_λ$的顶点，生产$ \ mathscr {k}（g）$的所有极值光线，这是$ \ mathscr {k}（g）$的点集，其中首先是coordication $ $λ$。我们表明，$ ip _ {\ varpi_i}的顶点随着来自圆锥$ \ Mathscr {k}（l）$与简单Levi子组相关的顶点的提升，具有简单的root $α_i$。作为推论，我们获得了所有极端射线的完整描述，以及根据类型和等级的方式描述了极端射线数量的多项式公式。
Let $\mathscr{K}(G)$ be the rational cone generated by pairs $(λ, μ)$ where $λ$ and $μ$ are dominant integral weights and $μ$ is a nontrivial weight space in the representation $V_λ$ of $G$. We produce all extremal rays of $\mathscr{K}(G)$ by considering the vertices of corresponding intersection polytopes $IP_λ$, the set of points in $\mathscr{K}(G)$ with first coordinate $λ$. We show that vertices of $IP_{\varpi_i}$ arise as lifts of vertices coming from cones $\mathscr{K}(L)$ associated to simple Levi subgroups possessing the simple root $α_i$. As corollaries we obtain a complete description of all extremal rays, as well as polynomial formulas describing the numbers of extremal rays depending on type and rank.
