论文标题
$ \ imath $量子组的Serre-lusztig关系
Serre-Lusztig relations for $\imath$quantum groups
论文作者
论文摘要
令$（\ bf u，\ bf u^\ imath）$为量子对称的kac-moody类型。 $ \ imath $量子组$ \ bf u^\ imath $和Universal $ \ imath $量子组$ \ wideTilde {\ bf u}^\ imath $可以看作是量子组的概括和drinfeld的概括，而drinfeld dubl ugheres $ \ wideDILDE {\ bf u} $。在本文中，我们根据$ \ imath $ divered powers制定并建立了$ \ imath $量子组的serre-lusztig关系，这是lusztig lusztig高阶serre for量子组的$ \ imath $ -Analog。在$ \ imath $量子组上，这对编织组对称性进行了申请。
Let $(\bf U, \bf U^\imath)$ be a quantum symmetric pair of Kac-Moody type. The $\imath$quantum groups $\bf U^\imath$ and the universal $\imath$quantum groups $\widetilde{\bf U}^\imath$ can be viewed as a generalization of quantum groups and Drinfeld doubles $\widetilde{\bf U}$. In this paper we formulate and establish Serre-Lusztig relations for $\imath$quantum groups in terms of $\imath$divided powers, which are an $\imath$-analog of Lusztig's higher order Serre relations for quantum groups. This has applications to braid group symmetries on $\imath$quantum groups.
