A Serre presentation for the $\mathrm{ı}$quantum groups

Let $(\mathbf{U},{\mathbf{U}}^{\mathbf{ı}})$ be a quasi-split quantum symmetric pair of arbitrary Kac-Moody type, where “quasi-split” means the corresponding Satake diagram contains no black node. We give a presentation of the $\mathrm{ı}$quantum group ${\mathbf{U}}^{\mathbf{ı}}$ with explicit $\mathrm{ı}$Serre relations. The verification of new $\mathrm{ı}$Serre relations is reduced to some new q-binomial identities. Consequently, ${\mathbf{U}}^{\mathbf{ı}}$ is shown to admit a bar involution under suitable conditions on the parameters.