Abstract:It is very well known that if is the simple -dimensional representation of , the category of representations , , is equivalent to the Temperley-Lieb category . Such categorical equivalences between tangle categories and categories of representations are rare. In this work we give a family of new equivalences by extending the above equivalence to one between the category of representations , where is a projective Verma module of and the type Temperley-Lieb category , realised as a subquotient of the tangle category of Freyd, Yetter, Reshetikhin, Turaev and others.

---

中文翻译：

---

纠缠类别和无限维𝑈_{𝑞}（𝔰𝔩_2）-模类别的等价性

摘要：这是很好的知道，如果是简单的维表示，陈述的范畴，是等同于Temperley的-利布类别。缠结类别和表示类别之间的这种类别等效性很少见。在这项工作中，我们通过将上述等价范围扩展到表示形式的类别之间，给出了一系列新的等价形式，其中表示形式的射影Verma模块和Temperley-Lieb类型的形式，实现为Freyd，Yetter缠结类别的子商，Reshetikhin，Turaev等。

---