论文标题
两色Ext soergel演算
The Two-Color Ext Soergel Calculus
论文作者
论文摘要
我们计算与无限/有限二面群相关的soergel双模型之间的ext组，以实现特征0，并表明它们是免费的右$ r- $模块。特别是，我们获得了不可分解的soergel双模型的Hochschild共同体学的显式图。然后，我们为相应的延伸增强soergel双模型的单体类别提供了图表呈现。 作为应用程序，我们明确计算homfly同源性/三个分级链接同源性$ \ overline {\ mathrm {hhh}} $ for connect两个hopf链接和负圆形链接$ t $ t（3，-3）$作为正确的$ r- $ modules。此外，我们表明，有限二面体类型的soergel双模型的Hochschild共同体分类Gomi的痕迹，在二面体环境中提供了Soergel的HOM公式的$ T- $类似物。
We compute Ext groups between Soergel Bimodules associated to the infinite/finite dihedral group for a realization in characteristic 0 and show that they are free right $R-$modules. In particular, we obtain an explicit diagrammatic basis for the Hochschild cohomology of indecomposable Soergel Bimodules. We then give a diagrammatic presentation for the corresponding monoidal category of Ext-enhanced Soergel Bimodules. As applications, we explicitly compute HOMFLY homology/triply graded link homology $\overline{\mathrm{HHH}}$ for the connect sum of two Hopf links and the negative torus link $T(3,-3)$ as right $R-$modules. Furthermore, we show that the Hochschild cohomology of Soergel Bimodules in finite dihedral type categorifies Gomi's trace, providing a $t-$analog of Soergel's Hom Formula in the dihedral setting.
