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

• Autores: Catharina Stroppel
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 70, Nº 3, 2004, págs. 643-658
• Idioma: inglés
• DOI: 10.1112/s0024610704005708
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• Resumen

  • 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.