论文标题
奇数两变量的soergel双模型和rouquier综合体
Odd two-variable Soergel bimodules and Rouquier complexes
论文作者
论文摘要
我们考虑了soergel双模型类别的奇数类似物。在奇数和两个变量中，与偶数偶数情况相比，转座双模模不能合并到生成的soergel双模模中，迫使一个类别具有较大的Grothendieck环。我们建立了合适的函子的双聚会性，并在奇数soergel类别和相关的单数Soergel 2类别的两种情况下开发图形分解。我们描述了鲁奎尔复合物的奇怪类似物，并在同型类别中建立了它们的可逆性。对于三个变量，产生soergel双模型的张量产物的直接和总和分解为Reidemeister III关系提供了构成同型类别的障碍。
We consider the odd analogue of the category of Soergel bimodules. In the odd case and already for two variables, the transposition bimodule cannot be merged into the generating Soergel bimodule, forcing one into a monoidal category with a larger Grothendieck ring compared to the even case. We establish biadjointness of suitable functors and develop graphical calculi in the 2-variable case for the odd Soergel category and the related singular Soergel 2-category. We describe the odd analogue of the Rouquier complexes and establish their invertibility in the homotopy category. For three variables, the absence of a direct sum decomposition of the tensor product of generating Soergel bimodules presents an obstacle for the Reidemeister III relation to hold in the homotopy category.
