Resumen de Composition factors of quotients of the universal enveloping algebra by primitive ideals

Catharina Stroppel

• Graded versions of the principal series modules of the category of a semisimple complex Lie algebra 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 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 . It can be seen that these graded versions of principal series representations are neither rigid nor Koszul modules.