Graded versions of the principal series modules of the category $\cO$ of a semisimple complex Lie algebra $\mg$ are defined. Their combinatorial descriptions are given by some Kazhdan–Lusztig polynomials. A graded version of the Duflo–Zhelobenko four-term exact sequence is proved. This gives results about composition factors of quotients of the universal enveloping algebra of $\mg$ by primitive ideals; in particular an upper bound is obtained for the multiplicities of such composition factors. Explicit descriptions are given of principal series modules for Lie algebras of rank $2$. It can be seen that these graded versions of principal series representations are neither rigid nor Koszul modules.