论文标题
代表戒指的诺森指数
The Knutson Index of the Representation Ring
论文作者
论文摘要
在本文中，我们研究了是否在HOPF代数上给定的简单模块，存在一个虚拟模块，以使它们的张量产品是常规模块。这与唐纳德·诺特森（Donald Knutson）的猜想有关，后来被萨维兹基（Savitskii）反驳和精致，并指出，对于有限群体的每个不可还原性格，存在一个虚拟特征，因此张量产品是常规的特征。我们还引入了Knutson索引，以衡量Knutson的猜想失败，讨论其代数特性，并将反示例提交给Savitskii的猜想。
In this paper, we study if, for a given simple module over a Hopf algebra, there exists a virtual module such that their tensor product is the regular module. This is related to a conjecture by Donald Knutson, later disproved and refined by Savitskii, stating that for every irreducible character of a finite group, there exists a virtual character such that their tensor product is the regular character. We also introduce the Knutson Index as a measure of Knutson's Conjecture failure, discuss its algebraic properties and present counter-examples to Savitskii's Conjecture.
