The combinatorial category of Andersen, Jantzen and Soergel and filtered moment graph sheaves

We give an overview on the series of articles (Fiebig and Lanini, Filtered moment graph sheaves, arXiv:1508.05579, 2015, Fiebig and Lanini, Periodic structures on affine moment graphs I: dualities and translation functors, arXiv: 1504.01699, 2015, Fiebig and Lanini, Periodic structures on affine moment graphs II: multiplicities and modular representations (in preparation)) that aims at introducing a new approach towards the "combinatorial" category introduced by Andersen, Jantzen and Soergel in their work on Lusztig's conjecture on the irreducible highest weight characters of modular algebraic groups