Quasi-split iYangians: minimalistic presentations and coideal structures
Abstract
We study iYangians, namely twisted Yangians in the Drinfeld current presentation, associated with quasi-split symmetric pairs of type ADE with nontrivial diagram involution. We establish minimalistic presentations in terms of degree-zero and degree-one generators. Type A2n is treated separately: the isolated rank-two case requires two additional relations, whereas in higher rank these relations are forced by the neighboring noncentral orbit. As a by-product, we strengthen Theorem 3.1 in arxiv:2511.07136 by proving that the extra relation in the minimalistic presentation of split iYangian is redundant whenever g has rank at least two. We also construct explicit injective homomorphisms from quasi-split iYangians into Yangians, identify their images as right coideal subalgebras, and obtain isomorphisms between the Drinfeld and J presentations. Finally, we derive triangular estimates for the Drinfeld currents and their coproducts and apply them to the imathℓ-weights arising by restriction from finite-dimensional Yangian modules.
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BibTeX
@misc{huang2026quasisplit,
title = {{Quasi-split iYangians: minimalistic presentations and coideal structures}},
author = {Binhe Huang and Kang Lu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08269},
eprint = {2609.08269},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08269},
}
RIS
TY - UNPB
TI - Quasi-split iYangians: minimalistic presentations and coideal structures
AU - Binhe Huang
AU - Kang Lu
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08269
UR - https://arxiv.org/abs/2609.08269
AB - We study iYangians, namely twisted Yangians in the Drinfeld current presentation, associated with quasi-split symmetric pairs of type ADE with nontrivial diagram involution. We establish minimalistic presentations in terms of degree-zero and degree-one generators. Type A_2n is treated separately: the isolated rank-two case requires two additional relations, whereas in higher rank these relations are forced by the neighboring noncentral orbit. As a by-product, we strengthen Theorem 3.1 in arxiv:2511.07136 by proving that the extra relation in the minimalistic presentation of split iYangian is redundant whenever g has rank at least two. We also construct explicit injective homomorphisms from quasi-split iYangians into Yangians, identify their images as right coideal subalgebras, and obtain isomorphisms between the Drinfeld and J presentations. Finally, we derive triangular estimates for the Drinfeld currents and their coproducts and apply them to the ^imathℓ-weights arising by restriction from finite-dimensional Yangian modules.
ER -