论文标题
$ \ mathfrak {sl} _ {2}^{+} $的2-陈述的张量2产生
A tensor 2-product of 2-representations of $\mathfrak{sl}_{2}^{+}$
论文作者
论文摘要
我们构建了一个明确的Abelian模型，用于张紧$ 2 $ 2 $ 2 $ 2 $ - 呈现$ \ Mathfrak {sl} _ {2}^{+} $的产品，特别是简单的$ 2 $ 2 $ - representation $ \ Mathcal {l}（1）$ 2 $ 2 $ 2 $ 2 $ 2-- $ \ Mathcal {V} $从代数的$ 2 $ - 类别中获取。我们在详细介绍了$ \ Mathcal {V} = \ Mathcal {l}（1）$的情况下，我们证明$ 2 $ - 产品在这种情况下会恢复预期的结构。我们的建筑部分验证了2008年的鲁奎尔的猜想。
We construct an explicit abelian model for the operation of tensor $2$-product of $2$-representations of $\mathfrak{sl}_{2}^{+}$, specifically the product of a simple $2$-representation $\mathcal{L}(1)$ with a given abelian $2$-representation $\mathcal{V}$ taken from the $2$-category of algebras. We study the case $\mathcal{V}=\mathcal{L}(1)$ in detail, and we show that the $2$-product in this case recovers the expected structure. Our construction partially verifies a conjecture of Rouquier from 2008.
