{"paper":{"title":"The Steinberg torus of a Weyl group as a module over the Coxeter complex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Marcelo Aguiar, T. Kyle Petersen","submitted_at":"2014-06-17T03:51:23Z","abstract_excerpt":"Associated to each irreducible crystallographic root system $\\Phi$, there is a certain cell complex structure on the torus obtained as the quotient of the ambient space by the coroot lattice of $\\Phi$. This is the Steinberg torus. A main goal of this paper is to exhibit a module structure on (the set of faces of) this complex over the (set of faces of the) Coxeter complex of $\\Phi$. The latter is a monoid under the Tits product of faces. The module structure is obtained from geometric considerations involving affine hyperplane arrangements. As a consequence, a module structure is obtained on t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4230","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}