Braid group action and quasi-split affine $\imath$quantum groups II: higher rank

Abstract

This paper studies quantum symmetric pairs $(\widetilde{\mathbf U}, \widetilde{{\mathbf U}}^\imath )$ associated with quasi-split Satake diagrams of affine type $A_{2r-1}, D_r, E_{6}$ with a nontrivial diagram involution fixing the affine simple node. Various real and imaginary root vectors for the universal $\imath$quantum groups $\widetilde{{\mathbf U}}^\imath$ are constructed with the help of the relative braid group action, and they are used to construct affine rank one subalgebras of $\widetilde{{\mathbf U}}^\imath$. We then establish relations among real and imaginary root vectors in different affine rank one subalgebras and use them to give a Drinfeld type presentation of $\widetilde{{\mathbf U}}^\imath$.