Quantum current algebras associated with rational $R$matrix
Abstract
We study quantum current algebra $\textrm{A}(\overline{R})$ associated with the rational $R$matrix of $\mathfrak{gl}_N$ and we give explicit formulae for the elements of its center at the critical level. Due to EtingofKazhdan's construction, the level $c$ vacuum module $\mathcal{V}_c(\overline{R})$ for the algebra $\textrm{A}(\overline{R})$ possesses a quantum vertex algebra structure for any complex number $c$. We prove that any module for the quantum vertex algebra $\mathcal{V}_c(\overline{R})$ is naturally equipped with a structure of restricted $\textrm{A}(\overline{R})$module of level $c$ and vice versa.
 Publication:

arXiv eprints
 Pub Date:
 January 2018
 arXiv:
 arXiv:1801.03543
 Bibcode:
 2018arXiv180103543K
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematical Physics;
 Mathematics  Representation Theory
 EPrint:
 27 pages, minor changes and corrections, final version