{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/on-the-minimal-modules-for-exceptional-lie","title":"On the minimal modules for exceptional Lie algebras: Jordan blocks and stabilisers","arxiv_id":"1508.02918","date":"2015-08-12","proceeding":null,"authors":["David I. Stewart"],"abstract":"Let G be a simple simple-connected exceptional algebraic group of type G_2, F_4, E_6 or E_7 over an algebraically closed field k of characteristic p>0 with \\g=Lie(G). For each nilpotent orbit G.e of \\g, we list the Jordan blocks of the action of e on the minimal induced module V_min of \\g. We also establish when the centralisers G_v of vectors v\\in V_min and stabilisers \\Stab_G<v> of 1-spaces <v>\\subset V_min are smooth; that is, when \\dim G_v=\\dim\\g_v or \\dim \\Stab_G<v>=\\dim\\Stab_\\g<v>.","url_abs":"https://arxiv.org/abs/1508.02918v6","url_pdf":"https://arxiv.org/pdf/1508.02918v6.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"on-the-minimal-modules-for-exceptional-lie","repo_url":"https://github.com/davistem/nilpotent_orbits_gap","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}