拟分裂 iYangian：极简表示与余理想结构
Quasi-split iYangians: minimalistic presentations and coideal structures
- Indiana University（印第安纳大学）
- Southern University of Science and Technology（南方科技大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究拟分裂对称对关联的 iYangian，给出极简表示，构造到 Yangian 的嵌入并识别余理想，证明表示同构，并推导电流三角估计以分析限制权。
AI中文摘要：
我们研究与具有非平凡图对合的 $\mathsf{ADE}$ 型拟分裂对称对相关联的 iYangian，即 Drinfeld 当前表示中的扭曲 Yangian。我们建立了由零次和一次生成元给出的极简表示。$\mathsf A_{2n}$ 型被单独处理：孤立的秩二情形需要两个附加关系，而在更高秩中，这些关系由相邻的非中心轨道强制得出。作为副产品，我们通过证明当 $\mathfrak g$ 的秩至少为 2 时，分裂 iYangian 的极简表示中的额外关系是多余的，从而加强了 arXiv:2511.07136 中的定理 3.1。我们还构造了从拟分裂 iYangian 到 Yangian 的显式单射同态，将其像识别为右余理想子代数，并获得了 Drinfeld 表示与 $J$ 表示之间的同构。最后，我们推导了 Drinfeld 电流及其余积的三角估计，并将其应用于由有限维 Yangian 模限制得到的 ${}^\imath\ell$-权。
英文摘要：
We study iYangians, namely twisted Yangians in the Drinfeld current presentation, associated with quasi-split symmetric pairs of type $\mathsf{ADE}$ with nontrivial diagram involution. We establish minimalistic presentations in terms of degree-zero and degree-one generators. Type $\mathsf A_{2n}$ 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 $\mathfrak g$ 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 ${}^\imath\ell$-weights arising by restriction from finite-dimensional Yangian modules.
