论文标题
$ \ imath $量子组及其振荡器表示的差异操作员方法
Differential operator approach to $\imath$quantum groups and their oscillator representations
论文作者
论文摘要
对于准切片的SATAKE图，我们定义了修改后的$ Q $ -Weyl代数，并表明它与相应的$ \ imath $ Quantum组之间存在代数同构。换句话说，我们为$ \ imath $量子组提供了一种不同的操作员方法。同时，获得了$ \ imath $量子组的振荡器表示。构建了这些振荡器表示的不可还原亚代表的晶体基础。
For a quasi-split Satake diagram, we define a modified $q$-Weyl algebra, and show that there is an algebra homomorphism between it and the corresponding $\imath$quantum group. In other words, we provide a differential operator approach to $\imath$quantum groups. Meanwhile, the oscillator representations of $\imath$quantum groups are obtained. The crystal basis of the irreducible subrepresentations of these oscillator representations are constructed.
