Representations of Super Yangians with Gelfand-Tsetlin bases

Abstract

The evaluation homomorphism from the super Yangian $\mathrm{Y}({\mathfrak{gl}}_{m|n})$ to the universal enveloping algebra $\mathrm{U}({\mathfrak{gl}}_{m|n})$ allows one to regard the ${\mathfrak{gl}}_{m|n}$-modules as $\mathrm{Y}({\mathfrak{gl}}_{m|n})$-modules. In this paper, we establish necessary and sufficient conditions for simple tensor products of covariant evaluation modules to be tame. We also provide an explicit construction of Gelfand-Tsetlin bases for tensor products of skew modules.