Gelfand-Tsetlin Bases of representations for super Yangian and quantum affine superalgebra

Abstract

We give explicit actions of Drinfeld generators on Gelfand-Tsetlin bases of super Yangian modules associated with skew Young diagrams. In particular, we give another proof that these representations are irreducible. We study irreducible tame \(\mathrm Y(\mathfrak{gl}_{1|1})\)-modules and show that a finite-dimensional irreducible \(\mathrm Y(\mathfrak{gl}_{1|1})\)-module is tame if and only if it is thin. We also give the analogous statements for quantum affine superalgebra of type A.