Minuscule Elements of Weyl Groups, the Numbers Game, andd-Complete Posets
Minuscule Elements of Weyl Groups, the Numbers Game, andd-Complete Posets
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外尔群的微小元素、数字游戏和 d-完全姿势集
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发表时间：
1999
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通讯作者：
Robert A. Proctor
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作者：
Robert A. Proctor
本文证明了与限制型Mozes数对策有关的某些偏序集是分配格。这些分配格的并不可约偏序集被刻画成局部结构性质的集合，这些性质构成了d -完全偏序集的定义。在表示论的语言中，单缀Kac-Moody代数的可积表示的权图的顶部“极小部分”被证明是分配格。这些晶格形成了弱Bruhat序的某个区间族。这些Bruhat格在研究Weyl群及其相关Schubert簇的λ-极小元的约化分解中是有用的。最近证明了d -完备偏序集同时具有钩长和Jeu de Taquin性质。
Abstract Certain posets associated to a restricted version of the numbers game of Mozes are shown to be distributive lattices. The posets of join irreducibles of these distributive lattices are characterized by a collection of local structural properties, which form the definition of d -complete poset. In representation theoretic language, the top “minuscule portions” of weight diagrams for integrable representations of simply laced Kac–Moody algebras are shown to be distributive lattices. These lattices form a certain family of intervals of weak Bruhat orders. These Bruhat lattices are useful in studying reduced decompositions of λ-minuscule elements of Weyl groups and their associated Schubert varieties. The d -complete posets have recently been proven to possess both the hook length and the jeu de taquin properties.