  Under certain conditions, we give an estimate from above on the number of
differential equations of order $r+1$ with prescribed regular singular points,
prescribed exponents at singular points, and having a quasi-polynomial flag of
solutions. The estimate is given in terms of a suitable weight subspace of the
tensor power $U(\n_-)^{\otimes (n-1)}$, where $n$ is the number of singular
points in $\C$ and $U(\n_-)$ is the enveloping algebra of the nilpotent
subalgebra of $\glg_{r+1}$.
