Parallelotope tilings and q-decomposition numbers

We provide closed formulas for a large subset of the canonical basis vectors of the Fock space representation of Uq(slˆe). These formulas arise from parallelotopes which assemble to form polytopal complexes. The subgraphs of the Ext1-quivers of v-Schur algebras at complex e-th roots of unity generated by simple modules corresponding to these canonical basis vectors are given by the 1-skeletons of the polytopal complexes.