A Drinfeld presentation for the twisted Yangian $Y_3^+$

TL;DR

This paper introduces a Drinfeld presentation for the twisted Yangian associated with a_3, defines shifted versions, and explores homomorphisms to universal enveloping algebras, conjecturing connections to finite W-algebras.

Contribution

It provides a new Drinfeld presentation for the twisted Yangian Y_3^+ and constructs shifted subalgebras with homomorphisms to other algebraic structures.

Findings

Defined Drinfeld generators for Y_3^+

Constructed shifted twisted Yangians and their homomorphisms

Conjectured isomorphisms with finite W-algebras

Abstract

We define the Drinfeld generators for $Y_3^+$, the twisted Yangian associated to the Lie algebra $\mathfrak{so}_3(\mathbb{C})$. This allows us to define shifted twisted Yangians, which are certain subalgebras of $Y_3^+$. We show that there are families of homomorphisms from the shifted twisted Yangians in $Y_3^+$ to the universal enveloping algebras of various orthogonal and symplectic Lie algebras, and we conjecture that the images of these homomorphisms are isomorphic to various finite $W$-algebras.