论文标题
$γ$颜色的微度posets和$ p $ -Minuscule kac-moody表示形式的分类
Classifications of $Γ$-colored minuscule posets and $P$-minuscule Kac--Moody representations
论文作者
论文摘要
$γ$颜色的$ d $ complete和$γ$颜色的缩影posets统一并概括了R.A.引入的多种彩色posets。 Proctor，J.R。Stembridge和R.M.绿色的。在先前的工作中，我们表明，$γ$颜色的微尺寸posets是必要的，足以从彩色posets构建kac--moody代数的某些代表，这些代数将半密布的lie代数的微小表示。在本文中，我们对$γ$颜色的微尺寸Posets进行了分类，这也对相应的表示形式进行了分类。我们表明，$γ$颜色的微度姿势是Proctor的彩色微小Posets和连接的全绿色绿色的彩色微小poset的截然不同的工会。连接的有限$γ$颜色的微尺寸posets可以实现为相应有限的谎言类型中的某些coroots。
The $Γ$-colored $d$-complete and $Γ$-colored minuscule posets unify and generalize multiple classes of colored posets introduced by R.A. Proctor, J.R. Stembridge, and R.M. Green. In previous work, we showed that $Γ$-colored minuscule posets are necessary and sufficient to build from colored posets certain representations of Kac--Moody algebras that generalize minuscule representations of semisimple Lie algebras. In this paper we classify $Γ$-colored minuscule posets, which also classifies the corresponding representations. We show that $Γ$-colored minuscule posets are precisely disjoint unions of colored minuscule posets of Proctor and connected full heaps of Green. Connected finite $Γ$-colored minuscule posets can be realized as certain posets of coroots in the corresponding finite Lie type.
