Relation between categories of representations of the super-Yangian of a special linear Lie superalgebra and quantum loop superalgebra

Abstract

Using the approach developed by Gautam and Toledano Laredo, we introduce analogues of the category $$ \mathfrak{O} $$ for representations of the Yangian $$Y_\hbar(A(m,n))$$ of a special linear Lie superalgebra and the quantum loop superalgebra $$U_q(LA(m,n))$$ . We investigate the relation between them and conjecture that these categories are equivalent.