Serre-Lusztig relations for ıquantum groups III

Let U˜ı be a quasi-split universal ıquantum group associated to a quantum symmetric pair (U˜,U˜ı) of Kac-Moody type with a diagram involution τ. We establish the Serre-Lusztig relations for U˜ı associated to a simple root i such that i≠τi, complementary to the Serre-Lusztig relations associated to i=τi which we obtained earlier. A conjecture on braid group symmetries on U˜ı associated to i disjoint from τi is formulated.