Representations of Super Yangians with Gelfand-Tsetlin bases

Abstract

The evaluation homomorphisms from the super Yangian $\Ymn$ to the universal enveloping algebra $\U(\gl_{m|n})$ allows one to regard the covariant tensor module of $\gl_{m|n}$ as $\Ymn$ 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 $\Y(\mathfrak{gl}_m)$. We give a necessary and sufficient condition for such modules to be tame, which generalizes the earlier work of Nazarov and Tarasov for $\Y(\mathfrak{gl}_m)$ to the super case.