2026/07/16 by Vidas Regelskis
Mathematics · #math.QA #math-ph #math.MP #math.RT
We study twisted Yangians associated with the split symmetric pairs of types BI, CI and DI. We introduce a new presentation of these algebras, which we call the transposed presentation, governed by a twisted reflection equation that interacts naturally with the Gaussian decomposition of the generating matrix. Working entirely within the R-matrix presentation, we derive Drinfeld-type current presentations of the special twisted Yangian SYtw(\mathfrakgN) and of the extended twisted Yangian Xtw(\mathfrakgN), in which the Serre relations are stated in a closed current form. Extracting coefficients recovers the Drinfeld presentation due to Lu. As a consequence, we establish the isomorphism between the R-matrix and Drinfeld presentations of these twisted Yangians conjectured by Lu, Wang and Zhang. As a byproduct, we obtain a tensor product decomposition of Xtw(\mathfrakgN) into the twisted Yangian in the Drinfeld presentation and a polynomial ring in countably many central variables. We also obtain Poincaré-Birkhoff-Witt bases in the Drinfeld generators and describe the coideal coproduct on the low Drinfeld modes.