Dynkin Diagram Classification of λ-Minuscule Bruhat Lattices and of d-Complete Posets
Dynkin Diagram Classification of λ-Minuscule Bruhat Lattices and of d-Complete Posets
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λ-微小 Bruhat 格子和 d-完全偏集的 Dynkin 图分类
DOI：
10.1023/a:1018615115006
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发表时间：
1999
影响因子：
0.8
通讯作者：
Robert A. Proctor
中科院分区：
文献类型：
--
作者：
Robert A. Proctor
抽象完备偏序集是指满足一定局部结构条件的偏序集。这些偏序集在代数组合学中扮演着几个角色，与形状，移位形状，平面划分和钩长偏序集的概念有关。它们也在李理论和代数几何中扮演了几个角色，涉及λ-极小元和简单缀条的一般Weyl或Coxeter群的Bruhat分配格，以及λ-极小Schubert簇。本文给出了用Dynkin图表示的d-完全偏序集的一种分类。
Abstractd-Complete posets are defined to be posets which satisfy certain local structural conditions. These posets play or conjecturally play several roles in algebraic combinatorics related to the notions of shapes, shifted shapes, plane partitions, and hook length posets. They also play several roles in Lie theory and algebraic geometry related to λ-minuscule elements and Bruhat distributive lattices for simply laced general Weyl or Coxeter groups, and to λ-minuscule Schubert varieties. This paper presents a classification of d-complete posets which is indexed by Dynkin diagrams.