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 Poincaré-Birkhoff-Witt(PBW) theorem for the quantum loop superalgebra ${\mathrm{U}}_q\left({\mathfrak{Lgl}}_{M|N}\right)$. 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 ${\mathrm{U}}_q\left({\mathfrak{Lgl}}_{M|2n}\right)$ with respect to the comultiplication.

34 pages, 2 figures.Comments are welcome!