Partial theta-series and branching rules for the $\text{sl}(3)$ parabolic Verma modules

The monodromy of the $\text{sl}(3)$ Casimir flat connection around root hyperplanes is studied. For the computation of the traces of the root monodromy operators, acting on the parabolic Verma modules, we deduce branching rules w.r.t. the corresponding root $\text{sl}(2)$ subalgebras. We show that the traces of the monodromy operators are partial theta functions of special type.