From quantum loop superalgebras to super Yangians

Abstract

The goal of this paper is to generalize a statement by Drinfeld, asserting that Yangians can be constructed as limit forms of the quantum loop algebras, to the super case. We establish a connection between quantum loop superalgebra and super Yangian of the general linear Lie superalgebra $\mathfrak{gl}_{M|N}$ in RTT type presentation. In particular, we derive the Poincar\'e-Birkhoff-Witt(PBW) theorem for the quantum loop superalgebra $\mathrm{U}_q\big(\mathfrak{Lgl}_{M|N}\big)$. Additionally, we investigate the application of the same argument to twisted super Yangian of the ortho-symplectic Lie superalgebra. For this purpose, we introduce the twisted quantum loop superalgebra as a one-sided coideal of $\mathrm{U}_q\big(\mathfrak{Lgl}_{M|2n}\big)$ with respect to the comultiplication.