The composition series of modules induced from Whittaker modules

  title={The composition series of modules induced from Whittaker modules},
  author={Dragan Mili{\vc}i{\'c} and Wolfgang Soergel},
  journal={Commentarii Mathematici Helvetici},
AbstractWe study a category of representations over a semisimple Lie algebra, which contains category $ \cal O $ as well as the so-called Whittaker modules, and prove a generalization of the Kazhdan-Lusztig conjectures in this context.  
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  • Inventiones
  • 1978
Tensor products of finite and infinite representations of semisimple Lie algebras
  • Compositio Math., 41:245–285,
  • 1980
algèbres enveloppantes
  • Cahiers Scientifiques, GauthierVillars,
  • 1974
Cahiers Scientifiques
  • GauthierVillars,
  • 1974
Cahiers Scientifiques
  • Gauthier-Villars,
  • 1974