A Drinfeld type presentation of twisted Yangians
Kang Lu, Weiqiang Wang, Weinan Zhang
TL;DR
This paper introduces a new Drinfeld type current presentation for twisted Yangians related to orthogonal Lie algebras, solving a longstanding open problem and enabling future research in this area.
Contribution
It develops a Gauss decomposition approach to establish a Drinfeld type presentation for twisted Yangians of type AI, which was previously unresolved.
Findings
Established a Drinfeld type current presentation for twisted Yangians.
Solved a longstanding open problem in the theory of twisted Yangians.
Potential to extend current presentations to other twisted Yangians.
Abstract
We develop a Gauss decomposition approach to establish a Drinfeld type current presentation for Olshanski's twisted Yangians associated to the orthogonal Lie algebras (also called twisted Yangians of type AI), settling a longstanding open problem. We expect that this will open the door for finding current presentations for other twisted Yangians.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Advanced Topics in Algebra