Serre–Lusztig Relations for ıQuantum Groups

Let ( U , U ı ) be a quantum symmetric pair of Kac–Moody type. The ı quantum groups U ı and the universal ı quantum groups U ~ ı can be viewed as a generalization of quantum groups and Drinfeld doubles U ~ . In this paper we formulate and establish Serre–Lusztig relations for ı quantum groups in terms of ı divided powers, which are an ı -analog of Lusztig’s higher order Serre relations for quantum groups. This has applications to braid group symmetries on ı quantum groups.