The combinatorics of category O for symmetrizable Kac-Moody algebras
arXiv:math/0305378
Abstract
We show that the structure of blocks outside the critical hyperplanes of category O over any symmetrizable Kac-Moody algebra depends only on the corresponding integral Weyl group and its action on the parameters of the Verma modules by giving a combinatorial description of the projective objects. As an application we derive the Kazhdan-Lusztig conjecture for non-integral blocks from the integral case in finite and affine situations.
23 pages, 1 figure. Revised version: Non-regular case corrected