Twisted Affine Yangian and Rectangular $W$-algebra of type $D$

TL;DR

This paper introduces a new algebraic structure called the twisted affine Yangian of type C and establishes a connection to rectangular W-algebras of type D, expanding the understanding of these complex algebraic objects.

Contribution

It defines the twisted affine Yangian of type C and constructs surjective homomorphisms to rectangular W-algebras of type D, revealing new algebraic relationships.

Findings

Established the twisted affine Yangian of type C.

Constructed surjective homomorphisms to rectangular W-algebras.

Connected algebraic structures of types C and D.

Abstract

We define the twisted affine Yangian of type $C$ and construct surjective homomorphisms from twisted affine Yangians of type $C$ to the universal enveloping algebra of the rectangular $W$-algebra associated with $\mathfrak{so}(ln)$ and a nilpotent element whose Jordan form corresponds to the partition $(l^n)$ in the case when $l$ and $n$ are even.