Twisted Yangians of quasi-split type DI and Drinfeld type current relations
Abstract
We study the twisted Yangian associated with the quasi-split symmetric pair (o2n, on−1⊕ on+1) of type DI. Working in the transposed R-matrix presentation of arXiv:2607.14692, we show that the generating matrix S(u) admits no Gaussian decomposition. We decompose instead the matrix Ŝ(u) = G S(u), where G is the constant term of S(u). A chain of quasi-determinantal embeddings lowers the rank within this family of pairs and ends at (o4,o3). Together with a direct study of a degenerate block of type AI, this gives a presentation of the special twisted Yangian SYtw(o2n,on−1⊕ on+1) by Drinfeld type current relations. The two fork nodes of the Dynkin diagram carry Drinfeld's presentation of Y(sl2). All other relations are those of split type DI, except that the Serre relation with a doubled fork node has zero right hand side. For n≥3 we obtain an explicit isomorphism between the R-matrix presentation of Guay and Regelskis and the Drinfeld presentation of Lu and Zhang. The Drinfeld generators are expressed through the Gaussian series of Ŝ(u). With quasi-split type AIII (Lu and Zhang), this completes the explicit comparison for the classical quasi-split types with a nontrivial diagram involution.
Related
- Twisted Yangians of split types BI, CI, 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 quasi-split type DI and Drinfeld type current relations}},
author = {Vidas Regelskis},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08357},
eprint = {2611.08357},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08357},
}
RIS
TY - UNPB
TI - Twisted Yangians of quasi-split type DI and Drinfeld type current relations
AU - Vidas Regelskis
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08357
UR - https://arxiv.org/abs/2611.08357
AB - We study the twisted Yangian associated with the quasi-split symmetric pair (o_2n, o_n−1⊕ o_n+1) of type DI. Working in the transposed R-matrix presentation of arXiv:2607.14692, we show that the generating matrix S(u) admits no Gaussian decomposition. We decompose instead the matrix Ŝ(u) = G S(u), where G is the constant term of S(u). A chain of quasi-determinantal embeddings lowers the rank within this family of pairs and ends at (o_4,o_3). Together with a direct study of a degenerate block of type AI, this gives a presentation of the special twisted Yangian SY^tw(o_2n,o_n−1⊕ o_n+1) by Drinfeld type current relations. The two fork nodes of the Dynkin diagram carry Drinfeld's presentation of Y(sl_2). All other relations are those of split type DI, except that the Serre relation with a doubled fork node has zero right hand side. For n≥3 we obtain an explicit isomorphism between the R-matrix presentation of Guay and Regelskis and the Drinfeld presentation of Lu and Zhang. The Drinfeld generators are expressed through the Gaussian series of Ŝ(u). With quasi-split type AIII (Lu and Zhang), this completes the explicit comparison for the classical quasi-split types with a nontrivial diagram involution.
ER -