The dual space of the Cartan subalgebra in a Kac–Moody algebra has a partial ordering defined by the rule that two elements are related if and only if their difference is a non-negative or non-positive integer linear combination of simple roots. In this paper, we study the subposet formed by dominant weights in affine Kac–Moody algebras. We give a more explicit description of the covering relations in this poset. We also study the structure of basic cells in this poset of dominant weights for untwisted affine Kac–Moody algebras of type A.

中文翻译：

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仿射Kac-Moody代数的主要权重格

Kac-Moody代数中Cartan子代数的对偶空间具有部分排序，该规则由以下规则定义：两个元素在且仅当它们的差是简单根的非负整数或正整数整数组合时才相关。在本文中，我们研究了仿射Kac-Moody代数中由支配权重形成的子代。我们对该坐姿中的覆盖关系进行更明确的描述。我们还研究了A型非扭转仿射Kac-Moody代数在该主要权重中的基本单元的结构。