Multiplet Classification and Invariant Differential Operators over the Lie Algebra $$F'_4$$

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact exceptional Lie algebra \(F'_4\) which is split real form of the exceptional Lie algebra \(F_4\). We consider induction from a maximal parabolic algebra. We classify the reducible Verma modules over \(F_4\) which are compatible with this induction. Thus, we obtain the classification of the corresponding invariant differential operators.