{"paper":{"title":"The Permutation Module on Flag Varieties in Cross Characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Junbin Dong, Xiaoyu Chen","submitted_at":"2017-07-09T15:15:03Z","abstract_excerpt":"Let ${\\bf G}$ be a connected reductive group over $\\bar{\\mathbb{F}}_q$, the algebraically closure of $\\mathbb{F}_q$ (the finite field with $q=p^e$ elements), with the standard Frobenius map $F$. Let ${\\bf B}$ be an $F$-stable Borel subgroup. Let $\\Bbbk$ be a field of characteristic $r\\neq p$. In this paper, we completely determine the composition factors of the induced module $Ind_{B}^{G}{tr}=\\Bbbk{G}\\otimes_{\\Bbbk{\\bf B}}$ tr (here $\\Bbbk{H}$ is the group algebra of the group ${H}$, and tr is the trivial $B$-module). In particular, we find a new family of infinite dimensional irreducible abst"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02592","kind":"arxiv","version":5},"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"}