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

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arxiv 2308.12484 v2 pith:TZI5YQ7P submitted 2023-08-24 math.QA math-phmath.MPmath.RT

Kang Lu This is my paper · ORCID
classification math.QAmath-phmath.MPmath.RT
keywords typeaffinegroupsimathquantumisomorphismpresentationtwisted
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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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Cited by 3 Pith papers

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

  1. Invariants of the extended twisted $h$-Yangian

    math.QA 2026-07 conditional novelty 6.0 of 10

    The extended twisted h-Yangian is shown to carry restricted-module and φ-coordinated quasi-module structures that yield central elements, invariants, and commutative families in the orthogonal and symplectic h-Yangians.

  2. 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...

  3. RTT presentation of coideal subalgebra of quantized enveloping algebra of type CI

    math.QA 2025-01 conditional novelty 6.0 of 10

    An RTT presentation and PBW basis are given for the type CI coideal subalgebra U_q^tw(gl_n) of U_q(sp_{2n}), together with an isomorphism to the i-quantum group and an explicit Poisson bracket.

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