论文标题
动力量子组的分类方法
A categorical approach to dynamical quantum groups
论文作者
论文摘要
我们在Harish-Chandra Bimodules的类别方面介绍了动态量子组的分类观点。我们证明了Tannaka二元定理的健忘函子，这是根据对双ggebroid的概念的略微修改，进入了Harish-Chandra Bimodules的单体类别。此外，我们表明，标准的动态量子组$ f（g）$和$ f_q（g）$与经典和量子Harish-chandra Bimodules的抛物线限制函数有关。最后，我们使用Zhelobenko操作员表现出抛物线限制函数的天然Weyl对称性，并表明它产生了动力学Weyl群的作用。
We present a categorical point of view on dynamical quantum groups in terms of categories of Harish-Chandra bimodules. We prove Tannaka duality theorems for forgetful functors into the monoidal category of Harish-Chandra bimodules in terms of a slight modification of the notion of a bialgebroid. Moreover, we show that the standard dynamical quantum groups $F(G)$ and $F_q(G)$ are related to parabolic restriction functors for classical and quantum Harish-Chandra bimodules. Finally, we exhibit a natural Weyl symmetry of the parabolic restriction functor using Zhelobenko operators and show that it gives rise to the action of the dynamical Weyl group.
