Minimalistic Presentation and Coideal Structure of Twisted Yangians

TL;DR

This paper presents a minimalistic Drinfeld type presentation for twisted Yangians linked to symmetric pairs, establishing their structure as right coideal subalgebras and relating generators to the Yangian.

Contribution

It introduces a new minimalistic presentation for twisted Yangians and proves their coideal structure and isomorphism with the J presentation of twisted Yangians.

Findings

Established an injective homomorphism from ${}^ ext{imath} ext{Y}$ to $ ext{Y}$

Identified ${}^ ext{imath} ext{Y}$ as a right coideal subalgebra of $ ext{Y}$

Provided estimates and descriptions of Drinfeld generators and coproduct images

Abstract

We introduce a minimalistic presentation for the twisted Yangian ${}^\imath\mathscr Y$ 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 ${}^\imath\mathscr Y$ to the Yangian $\mathscr Y$, thereby identifying ${}^\imath\mathscr Y$ as a right coideal subalgebra of $\mathscr Y$ and proving its isomorphism with the twisted Yangian in the $J$ presentation. Furthermore, we provide estimates for the Drinfeld generators of ${}^\imath\mathscr Y$ and describe their coproduct images in terms of the Drinfeld generators of $\mathscr Y$ under this identification.