  Recently, Gomez-Ullate et al. (1) have studied a particular N-particle
quantum problem with an elliptic function potential supplemented by an external
field. They have shown that the Hamiltonian operator preserves a finite
dimensional space of functions and as such is quasi exactly solvable (QES). In
this paper we show that other types of invariant function spaces exist, which
are in close relation to the algebraic properties of the elliptic functions.
Accordingly, series of new algebraic eigenfunctions can be constructed.
