论文标题
类型Q的量子网
Quantum Webs of Type Q
论文作者
论文摘要
网是用于在谎言（超级）代数和相关对象之间编码同构的组合图。本文将网理论扩展到Q型量子组。我们定义了量子类型Q网的单一超级类别，并表明它在$ u_q（\ Mathfrak {q} _N）$的$ u_q（\ mathfrak {q} _n）$的单体超级类别上接受了一个完整的滤波函数 - 由量子对称对称性的pemmetric pemmetric of the Natural of the Natural of the dual and dual and dual and dual and dual and dual。我们还表明，Web类别的某个子类别是功能区类别，并讨论了$ u_q（\ Mathfrak {q} _n）$的表示理论的应用程序，并与定向的，框架链接的不变性。
Webs are combinatorial diagrams used to encode homomorphisms between representations of Lie (super)algebras and related objects. This paper extends the theory of webs to the quantum group of type Q. We define a monoidal supercategory of quantum type Q webs and show it admits a full, essentially surjective functor onto the monoidal supercategory of $U_q(\mathfrak{q}_n)$-modules generated by the quantum symmetric powers of the natural representation and their duals. We also show that a certain subcategory of the web category is a ribbon category and discuss applications to the representation theory of $U_q(\mathfrak{q}_n)$ and to invariants of oriented, framed links.
