Abstract
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.
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