The Combinatorics of Category O over symmetrizable Kac-Moody Algebras
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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.
KeywordsTopological Group Weyl Group Verma Module Projective Object Integral Case
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