Jacobi–Trudi Identity and Drinfeld Functor for Super Yangian

Abstract

We show that the quantum Berezinian that gives a generating function of the integrals of motions of XXX spin chains associated to super Yangian $\textrm{Y}(\mathfrak{g}\mathfrak{l}_{m|n})$ can be written as a ratio of two difference operators of orders $m$ and $n$ whose coefficients are ratios of transfer matrices corresponding to explicit skew Young diagrams. In the process, we develop several missing parts of the representation theory of $\textrm{Y}(\mathfrak{g}\mathfrak{l}_{m|n})$ such as $q$-character theory, Jacobi–Trudi identity, Drinfeld functor, extended T-systems, and Harish-Chandra map.