On a Gelfand-Tsetlin representation of ${\mathfrak{s}\mathfrak{l}}_3$ in the space of sections of a local system with two monodromy parameters

We construct a Gelfand-Tsetlin representation of ${\mathfrak{s}\mathfrak{l}}_3$ in the space of sections of a local system. The local system lives on an open part of the flag variety given by the intersection of three translates of the big cell and has two complex monodromy parameters. We analyze the structure of this representation.