Minimalistic Presentation and Coideal Structure of Twisted Yangians

We introduce a minimalistic presentation for the twisted Yangian ${}^{\mathrm{ı}}\mathcal{Y}$ associated with split symmetric pairs (or Satake diagrams) introduced in arXiv:2406.05067 via a Drinfeld type presentation. As applications, we establish an injective algebra homomorphism from ${}^{\mathrm{ı}}\mathcal{Y}$ to the Yangian $\mathcal{Y}$, thereby identifying ${}^{\mathrm{ı}}\mathcal{Y}$ as a right coideal subalgebra of $\mathcal{Y}$ and proving its isomorphism with the twisted Yangian in the $J$ presentation. Furthermore, we provide estimates for the Drinfeld generators of ${}^{\mathrm{ı}}\mathcal{Y}$ and describe their coproduct images in terms of the Drinfeld generators of $\mathcal{Y}$ under this identification.