Transformation Groups

, Volume 11, Issue 1, pp 29–49

The Combinatorics of Category O over symmetrizable Kac-Moody Algebras


    • Mathematisches Institut, Universitat Freiburg, 79104 Freiburg

DOI: 10.1007/s00031-005-1103-8

Cite this article as:
Fiebig, P. Transformation Groups (2006) 11: 29. doi:10.1007/s00031-005-1103-8


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.

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© Birkhauser Boston 2006