论文标题
Gelfand-Cetlin类型还原的枚举
Enumeration of Gelfand-Cetlin type reduced words
论文作者
论文摘要
减少单词和换向类的组合在几何表示理论中起着重要作用。字符串polytope是与对称组中最长元素$ w_0 $的每个简化单词相关联的晶格多层，该元素编码了一个类型$ a $的谎言组的特定不可约定表示的字符。在本文中，我们为$ w_0 $的简化单词数量提供了递归公式，以使相应的字符串多层与gelfand-cetlin polytope相等。递归公式涉及变化形状的标准年轻tableaux的数量。我们还表明，每个换向等级都完全由称为索引的数量列表确定。
The combinatorics of reduced words and commutation classes plays an important role in geometric representation theory. A string polytope is a lattice polytope associated to each reduced word of the longest element $w_0$ in the symmetric group which encodes the character of a certain irreducible representation of a Lie group of type $A$. In this paper, we provide a recursive formula for the number of reduced words of $w_0$ such that the corresponding string polytopes are combinatorially equivalent to a Gelfand-Cetlin polytope. The recursive formula involves the number of standard Young tableaux of shifted shape. We also show that each commutation class is completely determined by a list of quantities called indices.
