论文标题
$ C_2 $中的Web计算和倾斜模块
Web Calculus and Tilting Modules in Type $C_2$
论文作者
论文摘要
使用Kuperberg的$ B_2/C_2 $ WEBS，然后遵循Elias和Libedinsky，我们描述了一种“轻叶”算法，以在$ \ Mathfrak的基本表示的任意张量产品之间构建形态的基础，以构建$ \ Mathfrak {so} so} _5 _5 \ cong \ cong \ cong \ mathfrak {sp} sp {sp} _44 $（和相关的量子组）。我们的论点几乎没有对基地的依赖。结果，我们证明，当$ [2] _q \ ne 0 $时，$ C_2 $ Web类别的Karoubi信封等于倾斜模块的类别。
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 $\mathcal{U}_q^{\mathbb{Z}}(\mathfrak{sp}_4)$.
