$C_2$类型中的Web演算和倾斜模
Web Calculus and Tilting Modules in Type $C_2$
摘要：
使用Kuperberg的$B_2/C_2$网，并遵循Elias和Libedinsky，我们描述了一个“光叶”算法来构建$\mathfrak{so}_5\cong \mathfrak{sp}_4$（和相关的量子群）的基本表示的任意张量积之间的态射的基础。我们的论证几乎不依赖于基本场。证明了当$[2]_q\ne 0$时，$C_2$网范畴的Karoubi包络等价于分幂量子群$\mathcal{U}_q^{\mathbb{Z}}(\mathfrak{sp}_4)$的倾斜模范畴.
英文摘要：
Using Kuperberg's $B_2/C_2$ webs, and following Elias and Libedinsky, we describe a "light leaves" algorithm to construct a basis of morphisms between arbitrary tensor products of fundamental representations for $\mathfrak{so}_5\cong \mathfrak{sp}_4$ (and the associated quantum group). Our argument has very little dependence on the base field. As a result, we prove that when $[2]_q\ne 0$, the Karoubi envelope of the $C_2$ web category is equivalent to the category of tilting modules for the divided powers quantum group $\mathcal{U}_q^{\mathbb{Z}}(\mathfrak{sp}_4)$.
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