论文标题
辫子组动作和准切片仿射$ \ imath $量子组我
Braid group action and quasi-split affine $\imath$quantum groups I
论文作者
论文摘要
这是准单行的两篇论文中的第一篇论文中的第一篇论文量子对称对$ \ big（\ widetilde {\ mathbf u}（\ wideHat {\ wideHat {\ mathfrak g}），\ wideTilde {\ wideTilde {\ mathbf U}^\ imath \ big）$ \ Mathfrak {Sl} _3 $配备了图形相关。我们明确构建了一个类型的相对辫子组动作$ a_2^{（2）} $上的相对辫子$ \ imath $ Quantum $ \ widetilde {\ Mathbf u}^\ imath $。构建了$ \ widetilde {\ mathbf u}^\ imath $的真实和虚构的矢量，然后建立了$ \ widetilde {\ mathbf u}^\ imath $的drinfeld类型表示。这为续集中的较高等级级仿射$ \ imath $量子组的德林菲尔德类型呈现提供了一种新的基本成分。
This is the first of two papers on quasi-split affine quantum symmetric pairs $\big(\widetilde{\mathbf U}(\widehat{\mathfrak g}), \widetilde{\mathbf U}^\imath \big)$, focusing on the real rank one case, i.e., $\mathfrak{g}= \mathfrak{sl}_3$ equipped with a diagram involution. We construct explicitly a relative braid group action of type $A_2^{(2)}$ on the affine $\imath$quantum group $\widetilde{\mathbf U}^\imath$. Real and imaginary root vectors for $\widetilde{\mathbf U}^\imath$ are constructed, and a Drinfeld type presentation of $\widetilde{\mathbf U}^\imath$ is then established. This provides a new basic ingredient for the Drinfeld type presentation of higher rank quasi-split affine $\imath$quantum groups in the sequel.
