Filtered modules on moment graphs and periodic patterns
We define and study a certain category that naturally arises from the quotient of an affine moment graph by the action of a root lattice. We show that it contains enough projectives and that the standard multiplicities of indecomposable projectives are given by Lusztig's periodic polynomials, if the characteristic of the ground field is zero or big enough. Then we relate it to the combinatorial category defined by Andersen, Jantzen and Soergel (and hence to the theory of G_1T-modules).