{"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/the-number-of-multiplicity-free-primitive","title":"The number of multiplicity-free primitive ideals associated with the rigid nilpotent orbits","arxiv_id":"2211.14581","date":"2022-11-26","proceeding":null,"authors":["Alexander Premet","David Stewart"],"abstract":"In this paper we describe the number of multiplicity-free primitive ideals associated with the rigid nilpotent orbits in finite-dimensional simple Lie algebras. Thanks to the results obtained earlier we need to solve the problem for the two largest rigid nilpotent orbits in Lie algebras of type ${\\rm E}_8$. As a corollary we compute the number of small modules in the corresponding reduced enveloping algebras over algebraically closed fields of characteristic $p>5$.","url_abs":"https://arxiv.org/abs/2211.14581v2","url_pdf":"https://arxiv.org/pdf/2211.14581v2.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":"the-number-of-multiplicity-free-primitive","repo_url":"https://github.com/davistem/the_number_of_multiplicity-free_primitive_ideals","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}