Quiver Yangian algebras associated to Dynkin diagrams of A-type and their rectangular representations

The connection between simple Lie algebras and their Yangian algebras has a long history. In this work, we construct finite-dimensional representations of Yangian algebras Y(slₙ) using the quiver approach. Starting from quivers associated to Dynkin diagrams of type A, we construct a family of quiver Yangians. We show that the quiver description of these algebras enables an effective construction of representations with a single non-zero Dynkin label. For these representations, we provide an explicit construction using the equivariant integration over the corresponding quiver moduli spaces. The resulting states admit a crystal description and can be identified with the Gelfand-Tsetlin bases for slₙ algebras. Finally, we show that the resulting Yangians possess notable algebraic properties, and the algebras are isomorphic to their alternative description known as the second Drinfeld realization.