A note on constructing quasi modules for quantum vertex algebras from twisted Yangians
Abstract
In this note, we consider the twisted Yangians $\text{Y}(\mathfrak{g}_N)$ associated with the orthogonal and symplectic Lie algebras $\mathfrak{g}_N=\mathfrak{o}_N,\mathfrak{sp}_N$. First, we introduce a certain subalgebra $\text{A}_c(\mathfrak{g}_N)$ of the double Yangian for $\mathfrak{gl}_N$ at the level $c\in\mathbb{C}$, which contains the centrally extended $\text{Y}(\mathfrak{g}_N)$ at the level $c$ as well as its vacuum module $\mathcal{M}_c(\mathfrak{g}_N)$. Next, we employ its structure to construct examples of quasi modules for the quantum affine vertex algebra $\mathcal{V}_c(\mathfrak{gl}_N)$ associated with the Yang $R$matrix. Finally, we use the description of the center of $\mathcal{V}_c(\mathfrak{gl}_N)$ to obtain explicit formulae for families of central elements for a certain completion of $\text{A}_c(\mathfrak{g}_N)$ and invariants of $\mathcal{M}_c(\mathfrak{g}_N)$.
 Publication:

arXiv eprints
 Pub Date:
 October 2022
 DOI:
 10.48550/arXiv.2210.12510
 arXiv:
 arXiv:2210.12510
 Bibcode:
 2022arXiv221012510K
 Keywords:

 Mathematics  Quantum Algebra
 EPrint:
 16 pages