{"paper":{"title":"Representations and primitive central idempotents of a finite solvable group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ravi S. Kulkarni, Soham Swadhin Pradhan","submitted_at":"2018-10-09T11:12:40Z","abstract_excerpt":"Let $G$ be a finite solvable group. Then $G$ always has a useful presentation, which we call a \"long presentation\". Using a \"long presentation\" of $G$, we present an inductive method of constructing the irreducible representations of $G$ over $\\mathbb{C}$ and computing the primitive central idempotents of the complex group algebra $\\mathbb{C}[G]$. For a finite abelian group, we present a systematic method of constructing the irreducible representations over a field of characteristic either $0$ or prime to order of the group and also a systematic method of computing the primitive central idempo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04166","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"}