论文标题
C型的C-Trees和连贯的表现，用于C型的多型
C-trees and a coherent presentation for the plactic monoid of type C
论文作者
论文摘要
在本文中，我们通过有限收敛呈现$ acol $ aCOL $，带有生成套装$ acol（c_n）$的$ contratigent $ c $ type $ c $的$ \ mathbb {n} - $装饰的$ c $ type $ c $的多理性胶片。通过Squier的连贯完成定理，通过识别产生汇合的家族，即产生$ 3- $单元，将此介绍扩展到连贯的演示文稿中。在这里，生成$ 3- $的单元是长度$ 3 $的关键分支。我们将晶体结构的概念调整为$ ACOL（C_N）^\ ast $，并证明$ 3- $单元的形状由Kashiwara操作员的作用保留。因此，我们将对连贯性呈现的研究减少到仅描述其源为最高词的生成$ 3- $单元。然后，我们介绍称为$ c- $树的组合对象，该对象在$ acol（c_n）^\ ast $中参数化最高权重的单词。 $ c- $树允许用Lecouvey介绍的类型$ c $中的插入算法来简化计算，我们证明，以$ acol $的形式生成$ 3- $的单元最多是$（4,3）$。结果，我们表明，正如Hage介绍的$ PL（C_N）$的列表示，最多生成了$ 3- $的形状单元格（4,3）$。这与$ a $ $ a $的情况进行了对比，其中$ pl（a_n）$的$ 3- $单元最多是$（3,3）$的形状。
In this article we introduce the $\mathbb{N}-$decorated plactic monoid of type $C$, denoted $Pl^\mathbb{N}(C_n)$, via a finite convergent presentation $ACol$, with generating set $ACol(C_n)$ consisting of admissible columns, and an element $ε$. By Squier's coherent completion theorem, this presentation is extended into a coherent presentation by identifying a family of generating confluences, i.e. generating $3-$cells. Here the generating $3-$cells are critical branchings on words of length $3$. We adapt the notions of crystal structure to $ACol(C_n)^\ast$ , and show that the shape of $3-$cells is preserved by the action of Kashiwara operators. Thus we reduce the study of the coherent presentation to only describing the generating $3-$cells whose source is a word of highest weight. We then introduce combinatorial objects called $C-$trees which parameterize the words of highest weight in $ACol(C_n)^\ast$. The $C-$trees allow for simplifying calculations with the insertion algorithm in type $C$, as introduced in by Lecouvey, and we prove that the generating $3-$cells in $ACol$ are of shape at most $(4,3)$. As a consequence, we show that the column presentation of $Pl(C_n)$, as introduced by Hage, has generating $3-$cells of shape at most $(4,3)$. This contrasts the situation in type $A$, where the $3-$cells in the column presentation of $Pl(A_n)$ are of shape at most $(3,3)$.
