Affine \(\imath \)Quantum Groups and Twisted Yangians in Drinfeld Presentations

IF 2.2 1区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL
Kang Lu, Weiqiang Wang, Weinan Zhang
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引用次数: 0

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.

仿射\(\imath \)量子群和扭曲yangian在Drinfeld的表现
我们通过对仿射\(\imath \)量子群(与分裂的Satake图相关)的Drinfeld表示的退化,在电流发生器和关系中构造了一类代数,扭曲的yangian(分裂型)。这些新代数承认PBW型基,并被证明是扭曲电流代数的一种变形;还提供了扭曲电流代数的介绍。对于AI型,它与通过高斯分解得到的扭曲Yangian的Drinfeld表示相匹配。我们推测,我们的分裂扭扬算子与RTT表示中的对应杨算子是同构的。
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来源期刊
Communications in Mathematical Physics
Communications in Mathematical Physics 物理-物理:数学物理
CiteScore
4.70
自引率
8.30%
发文量
226
审稿时长
3-6 weeks
期刊介绍: The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.
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