论文标题
Khovanov-Rozansky同源性的单粒模型
Monodromic model for Khovanov-Rozansky homology
论文作者
论文摘要
我们根据第一作者和Yun先前研究的单粒子Hecke类别描述了Soergel Bimodules的Hochschild共同体的新几何模型。此外，我们确定代表单个Hochschild共同体学组的对象（对于零和最高学位的共同体，这将减少到Gorsky，Hogancamp，Mellit和Nakagane的早期结果）。这些对象证明与与Weyl群反射表示的外部力量相对应的显式特征或相对的显式角色紧密相关。将所描述的函子应用于A型Hecke类别中的编织图像，我们获得了Khovanov-Rozansky结的几何描述，与Webster和Williamson之前考虑的基本不同。
We describe a new geometric model for the Hochschild cohomology of Soergel bimodules based on the monodromic Hecke category studied earlier by the first author and Yun. Moreover, we identify the objects representing individual Hochschild cohomology groups (for the zero and the top degree cohomology this reduces to an earlier result of Gorsky, Hogancamp, Mellit and Nakagane). These objects turn out to be closely related to explicit character sheaves corresponding to exterior powers of the reflection representation of the Weyl group. Applying the described functors to the images of braids in the Hecke category of type A we obtain a geometric description for Khovanov-Rozansky knot homology, essentially different from the one considered earlier by Webster and Williamson.
