论文标题
分类量子组的伴随作用
Categorification of the adjoint action of quantum groups
论文作者
论文摘要
让$ u $成为量化的包围代数。我们考虑$ u^+$的$ u $ $ u $的$ \ mathfrak {sl} _2 $ -subalgebra的伴随动作，这对于此操作最大化。我们在Quiver Hecke代数的上下文中对此表示形式进行分类。我们在Quiver Hecke代数的某些标准上获得了与$ \ Mathfrak {SL} _2 $相关的2类的动作。我们的方法与Kang-Kashiwara的方法相似，用于通过环形箭量Hecke代数对最高权重模块的分类。主要的新特征之一是分类作用与单体结构的兼容性，将代数上的派生概念分类。作为我们的某些结果的应用，我们将高阶量子关系关系分类，将Stošić的结果扩展到非简单的情况。
Let $U$ be a quantized enveloping algebra. We consider the adjoint action of an $\mathfrak{sl}_2$-subalgebra of $U$ on a subalgebra of $U^+$ that is maximal integrable for this action. We categorify this representation in the context of quiver Hecke algebras. We obtain an action of the 2-category associated with $\mathfrak{sl}_2$ on a category of modules over certain quotients of quiver Hecke algebras. Our approach is similar to that of Kang-Kashiwara for categorifications of highest weight modules via cyclotomic quiver Hecke algebras. One of the main new features is a compatibility of the categorical action with the monoidal structure, categorifying the notion of derivation on an algebra. As an application of some of our results, we categorify the higher order quantum Serre relations, extending results of Stošić to the non simply-laced case.
