张量积代数的迹去范畴化
Trace decategorification of tensor product algebras
摘要：
证明了在ADE型中，量子群的不可约项的张量积的Webster分类的迹同构于当前代数$\dot{U}(\mathfrak{g}[t])$的Weyl模的张量积.这推广了Beliakova、Habiro、Lauda和Webster的结果，他们证明了范畴化的量子群$\dot{\mathcal{U}}^*(\mathfrak{g})$的迹同构于$\dot{U}(\mathfrak{g}[t])$，而$\dot{\mathcal{U}}^*(\mathfrak{g})$的分圆商的迹（它范畴化了量子群的一个不可约的）同构于$\dot{U}(\mathfrak{g}[t])$的Weyl模。我们使用的变形参数的基础上韦伯斯特的技术展开2表示。
英文摘要：
We show that in ADE type the trace of Webster's categorification of a tensor product of irreducibles for the quantum group is isomorphic to a tensor product of Weyl modules for the current algebra $\dot{U}(\mathfrak{g}[t])$. This extends a result of Beliakova, Habiro, Lauda, and Webster who showed that the trace of the categorified quantum group $\dot{\mathcal{U}}^*(\mathfrak{g})$ is isomorphic to $\dot{U}(\mathfrak{g}[t])$, and the trace of a cyclotomic quotient of $\dot{\mathcal{U}}^*(\mathfrak{g})$, which categorifies a single irreducible for the quantum group, is isomorphic to a Weyl module for $\dot{U}(\mathfrak{g}[t])$. We use a deformation argument based on Webster's technique of unfurling 2-representations.
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