Malvenuto-Albertenauer代数的群塔分类
A categorification of the Malvenuto--Reutenauer algebra via a tower of groups
摘要：
用代数塔的模（或者更好地用群塔的表示论）来分类组合霍普夫代数有着悠久的传统。从组合学的观点来看，这样的分类提供了规范基、内积和证明正性结果的自然途径。超特征标理论的最新思想使得将群塔的表示论塑造成一个霍普夫结构变得更加容易。本文将这一程序应用于Malvenuto-Littenauer霍普夫代数。特别是，我们设计函子的表示论的塔的$p$ -群，实现了Hopf结构的Malvenuto--Alternauer代数的方式，其著名的基本基础对应于一个超特征的基础。
英文摘要：
There is a long tradition of categorifying combinatorial Hopf algebras by the modules of a tower of algebras (or even better via the representation theory of a tower of groups). From the point of view of combinatorics, such a categorification supplies canonical bases, inner products, and a natural avenue to prove positivity results. Recent ideas in supercharacter theory have made fashioning the representation theory of a tower of groups into a Hopf structure more tractable. This paper applies such a program to the Malvenuto--Reutenauer Hopf algebra. In particular, we design functors on the representation theory of a tower of $p$-groups that realize the Hopf structure of the Malvenuto--Reutenauer algebra in such a way that its well-known fundamental basis corresponds to a supercharacter basis.
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