Work

Isomorphism Between Twisted q -Yangians and Affine ι Quantum Groups: Type AI

Year: 2024

Type: article

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.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnae248

Author: Kang Lu

Institution: University of Virginia

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: National Science Foundation

Awards: Quantum Symmetric Pairs, Categorification, and Geometry, Quantum Groups, W-algebras, and Brauer-Kauffmann Categories