Representations of Super Yangians with Gelfand-Tsetlin bases

The evaluation homomorphisms from the super Yangian $\text{Ymn}$ to the universal enveloping algebra $\text{U}({\text{gl}}_{m\mathrm{\mid }n})$ allows one to regard the covariant tensor module of ${\text{gl}}_{m\mathrm{\mid }n}$ as $\text{Ymn}$ modules. We study simple quotients of the submodules generated by a tensor product of highest weight vectors inside the tensor products of covariant evaluation modules. In the case $n=0$, this recover all finite-dimensional simple modules of $\text{Y}({\mathfrak{g}\mathfrak{l}}_m)$. We give a necessary and sufficient condition for such modules to be tame, which generalizes the earlier work of Nazarov and Tarasov for $\text{Y}({\mathfrak{g}\mathfrak{l}}_m)$ to the super case.