Affine $\imath$quantum groups and twisted Yangians in Drinfeld presentations

TL;DR

This paper introduces a new family of twisted Yangian algebras derived from affine $ extit{ extbf{imath}}$quantum groups, providing PBW bases and connecting them to twisted current algebras and Yangians.

Contribution

It formulates twisted Yangians via degeneration of Drinfeld presentations, establishes PBW bases, and links to twisted current algebras and known Yangian presentations.

Findings

New algebraic structures with PBW bases

Connections between twisted Yangians and twisted current algebras

Matching with known Yangian presentations in specific cases

Abstract

We formulate a family of algebras, twisted Yangians (of split type) in current generators and relations, via a degeneration of the Drinfeld presentation of affine $\imath$quantum groups (associated with split Satake diagrams). These new algebras admit PBW type bases and are shown to be a deformation of twisted current algebras; presentations for twisted current algebras are also provided. For type AI, it matches with the Drinfeld presentation of twisted Yangian obtained via Gauss decomposition. We conjecture that our split twisted Yangians are isomorphic to the corresponding ones in RTT presentation.