Parallelotope tilings and $q$-decomposition numbers

Abstract

We provide closed formulas for a large subset of the canonical basis vectors of the Fock space representation of $U_q({\widehat{\mathfrak{sl}}}_e)$. These formulas arise from parallelotopes which assemble to form polytopal complexes. The subgraphs of the ${\mathrm{Ext}}^1$-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.

72 pages, 11 figures

References in corpus (1)

• Graded decomposition numbers for cyclotomic Hecke algebras