Isomorphism Between Twisted <i>q</i> -Yangians and Affine <i>ι</i> Quantum Groups: Type AI

Abstract By employing Gauss decomposition, we establish a direct and explicit isomorphism between the twisted $q$-Yangians (in R-matrix presentation) and affine $\imath $quantum groups (in current presentation) associated to symmetric pair of type AI introduced by Molev–Ragoucy–Sorba and Lu–Wang, respectively. As a corollary, we obtain a PBW-type basis for affine $\imath $quantum groups of type AI.