论文标题
Delannoy类别
The Delannoy category
论文作者
论文摘要
令$ g $为真实行的所有保留订单的自图的组。在以前的工作中，前两位作者构建了一个前塔纳基人类别$ \ usewiensline {\ mathrm {rep}}}}（g）$与$ g $相关的$。本文是对此类别的详细研究，我们将其命名为Delannoy类别。我们对简单对象进行分类，确定分支规则以打开子组，并为张量产品提供组合规则。 Delannoy类别具有一些显着的特征：它在所有特征上都是半简单的；所有类似物都有分类尺寸$ \ pm 1 $; Adams在其Grothendieck集团上的行动很琐碎。我们还基于Delannoy Paths提供了$ \ usewrm {rep}}（g）$的$ \下划线{\ mathrm {rep}} $的组合模型。
Let $G$ be the group of all order-preserving self-maps of the real line. In previous work, the first two authors constructed a pre-Tannakian category $\underline{\mathrm{Rep}}(G)$ associated to $G$. The present paper is a detailed study of this category, which we name the Delannoy category. We classify the simple objects, determine branching rules to open subgroups, and give a combinatorial rule for tensor products. The Delannoy category has some remarkable features: it is semi-simple in all characteristics; all simples have categorical dimension $\pm 1$; and the Adams operations on its Grothendieck group are trivial. We also give a combinatorial model for $\underline{\mathrm{Rep}}(G)$ based on Delannoy paths.
