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Affine $\imath$quantum groups and twisted Yangians in Drinfeld presentations

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arxiv 2406.05067 v2 pith:5HXI26RA submitted 2024-06-07 math.QA math-phmath.MPmath.RT

Kang Lu , Weiqiang Wang , Weinan Zhang This is my paper · ORCID
classification math.QAmath-phmath.MPmath.RT
keywords twistedalgebrascurrentdrinfeldpresentationsplittypeyangians
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abstract

We formulate a family of algebras, twisted Yangians (of split type) in current generators and relations, via a degeneration of the Drinfeld presentation of affine $\imath$quantum groups (associated with split Satake diagrams). These new algebras admit PBW type bases and are shown to be a deformation of twisted current algebras; presentations for twisted current algebras are also provided. For type AI, it matches with the Drinfeld presentation of twisted Yangian obtained via Gauss decomposition. We conjecture that our split twisted Yangians are isomorphic to the corresponding ones in RTT presentation.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Twisted Yangians of types BI, CI, DI and Drinfeld type current relations

    math.QA 2026-07 conditional novelty 6.0 of 10

    For split types BI, CI, DI, the R-matrix and Drinfeld current presentations of twisted Yangians are isomorphic, confirming the Lu–Wang–Zhang conjecture, with closed-form Serre relations, PBW bases, and a tensor-factor...

  2. Finite-dimensional irreducible representations of twisted loop algebras of the second kind

    math.RT 2025-06 conditional novelty 5.0 of 10

    Finite-dimensional irreducible representations of twisted loop algebras of the second kind are classified by explicit highest-weight power-sum formulas, proved elementarily for four minimal algebras and assembled in a...

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