Résume | Moment graph techniques have been applied in the study of non-critical blocks of category O for affine Kac-Moody algebras, while in the critical case these methods have not been developed yet. Inspired by the fact that non-critical representations are controlled by the Hecke algebra H, while critical level representations are expected to be governed by the periodic module M, we prove the moment graph analogue of a result by Lusztig which bridges H and M, and believe that it should provide us with new tools to attack the critical level case. |