标题： 混乱的辫子和iquantum Brauer范畴 显示英文标题

标题： The disoriented skein and iquantum Brauer categories

摘要： 我们开发了一种图示方法，用于研究正交对称李超代数在一般线性李超代数内部的量子对称对的表示理论。 我们的方法基于一种称为非定向辫子范畴的结构，我们将其定义为框架HOMFLYPT辫子范畴上的模范畴。 非定向辫子范畴可以全息地映射到对应于量子对称对的量子包络代数的模范畴，并且可以被视为这些模范畴之间的插值范畴。 在赋予后者框架HOMFLYPT辫子范畴上的模范畴结构之后，我们定义了非定向辫子范畴与量子Brauer范畴（也称为$q$-Brauer范畴）之间的模范畴等价。 非定向辫子范畴相较于量子Brauer范畴具有优势，它具有对偶结构，并允许全息函子作为模范畴的严格同态。 最后，我们构建了非定向辫子范畴和量子Brauer范畴的态射空间的显式基底。 显示英文摘要

摘要： We develop a diagrammatic approach to the representation theory of the quantum symmetric pairs corresponding to orthosymplectic Lie superalgebras inside general linear Lie superalgebras. Our approach is based on the disoriented skein category, which we define as a module category over the framed HOMFLYPT skein category. The disoriented skein category admits full incarnation functors to the categories of modules over the iquantum enveloping algebras corresponding to the quantum symmetric pairs, and it can be viewed as an interpolating category for these categories of modules. We define an equivalence of module categories between the disoriented skein category and the iquantum Brauer category (also known as the $q$-Brauer category), after endowing the latter with the structure of a module category over the framed HOMFLYPT skein category. The disoriented skein category has some advantages over the iquantum Brauer category, possessing duality structure and allowing the incarnation functors to be strict morphisms of module categories. Finally, we construct explicit bases for the morphism spaces of the disoriented skein and iquantum Brauer categories.