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Isomorphism between twisted $q$-Yangians and affine $\imath$quantum groups: type AI (2308.12484v2)
Published 24 Aug 2023 in math.QA, math-ph, math.MP, and math.RT
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.