Twisted Yangians of split types BI, CI, DI and Drinfeld type current relations
Abstract
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(gN) and of the extended twisted Yangian Xtw(gN), in which the Serre relations are stated in a closed current form. Extracting coefficients recovers the Drinfeld presentation of Lu, Wang and Zhang, in the normalisation of Lu. As a consequence, we establish an explicit isomorphism between the R-matrix and Drinfeld presentations conjectured by Lu, Wang and Zhang. As a byproduct, we obtain a tensor product decomposition of Xtw(gN) 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 the coideal coproduct on the low Drinfeld modes at all but the last node.
Related
- Twisted Yangians of quasi-split type DI and Drinfeld type current relations
- Quivers with Involutions and Shifted Twisted Yangians via Coulomb Branches
- Classification of twisted Yangians as coideal subalgebras of Yangians
- Confluence relations, Hoffman basis over \mathbb{Z}_{(2)}, and the Deligne--Drinfeld conjecture
- Classification of finite-dimensional Nichols algebras of rank two in twisted Yetter--Drinfeld categories
BibTeX
@misc{regelskis2026twisted,
title = {{Twisted Yangians of split types BI, CI, DI and Drinfeld type current relations}},
author = {Vidas Regelskis},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.14692},
eprint = {2607.14692},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.14692},
}
RIS
TY - UNPB
TI - Twisted Yangians of split types BI, CI, DI and Drinfeld type current relations
AU - Vidas Regelskis
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2607.14692
UR - https://arxiv.org/abs/2607.14692
AB - 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 SY^tw(g_N) and of the extended twisted Yangian X^tw(g_N), in which the Serre relations are stated in a closed current form. Extracting coefficients recovers the Drinfeld presentation of Lu, Wang and Zhang, in the normalisation of Lu. As a consequence, we establish an explicit isomorphism between the R-matrix and Drinfeld presentations conjectured by Lu, Wang and Zhang. As a byproduct, we obtain a tensor product decomposition of X^tw(g_N) 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 the coideal coproduct on the low Drinfeld modes at all but the last node.
ER -