Transformation Groups

, Volume 11, Issue 1, pp 29–49 | Cite as

The Combinatorics of Category O over symmetrizable Kac-Moody Algebras

  • Peter FiebigEmail author


We show that the structure of a block outside the critical hyperplanes of category O over a symmetrizable Kac-Moody algebra depends only on the corresponding integral Weyl group and its action on the parameters of the Verma modules. This is done by giving a combinatorial description of the projective objects in the block. As an application, we derive the Kazhdan-Lusztig conjecture for nonintegral blocks from the integral case for finite or affine Weyl groups. We also prove the uniqueness of Verma embeddings outside the critical hyperplanes.


Topological Group Weyl Group Verma Module Projective Object Integral Case 
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Copyright information

© Birkhauser Boston 2006

Authors and Affiliations

  1. 1.Mathematisches Institut, Universitat Freiburg, 79104 FreiburgGermany

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