论文标题
E3融合 - 卷积型产品的模型，可构造滑轮上
A model for the E3 fusion-convolution product of constructible sheaves on the affine Grassmannian
论文作者
论文摘要
让$ g $成为一个复杂的还原组。 $ g $的球形Hecke类别可以作为$ g _ {\ Mathcal O} $的类别显示 - extine grassmannian $ \ mathrm {gr} _g $上的equivariant可构造sheaves。该类别承认卷积产品，扩展了卷积的卷积产品。在本文中，我们将提到的卷积产品升级为$ \ infty $ - 类别中的左T型$ \ Mathbb e_3 $ -monoidal结构。该构造是自态侧的固有的。我们的主要工具是Beilinson - Drinfeld Grassmannian，Lurie通过拓扑ran空间，分层空间的同型理论和对应关系的形式主义的$ \ Mathbb e_k $ -algebras的特征。
Let $G$ be a complex reductive group. The spherical Hecke category of $G$ can be presented as the category of $G_{\mathcal O}$-equivariant constructible sheaves on the affine Grassmannian $\mathrm{Gr}_G$. This category admits a convolution product, extending the convolution product of equivariant perverse sheaves. In this paper, we upgrade the mentioned convolution product to a left t-exact $\mathbb E_3$-monoidal structure in $\infty$-categories. The construction is intrinsic to the automorphic side. Our main tools are the Beilinson--Drinfeld Grassmannian, Lurie's characterization of $\mathbb E_k$-algebras via the topological Ran space, the homotopy theory of stratified spaces, and the formalism of correspondences.
