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arXiv · 2308.12484

Isomorphism between twisted $q$-Yangians and affine $\imath$quantum groups: type AI

Kang Lu
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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.

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Kang Lu. 2023-08-24. Isomorphism between twisted $q$-Yangians and affine $\imath$quantum groups: type AI. https://doi.org/10.1093/imrn%2Frnae248

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