Invariant Differential Operators for the Real Exceptional Lie Algebra $F_4^{\mathrm{\prime }}$

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 $F_4^{\mathrm{\prime }}=F_{4(4)}$ 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.