{"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/an-investigation-into-lie-algebra","title":"An investigation into Lie algebra representations obtained from regular holonomic D-modules","arxiv_id":"2111.14774","date":"2021-11-29","proceeding":null,"authors":["Julian Wykowski","Travis Schedler"],"abstract":"Beilinson--Bernstein localisation relates representations of a Lie algebra $\\mathfrak{g}$ to certain $\\mathcal{D}$-modules on the flag variety of $\\mathfrak{g}$. In [arXiv:2002.01540], examples of $\\mathfrak{sl}_2$-representations which correspond to $\\mathcal{D}$-modules on $\\mathbb{CP}^1$ were computed. In this expository article, we give a topological description of these and extended examples via the Riemann-Hilbert correspondence. We generalise this to a full characterisation of $\\mathfrak{sl}_2$-representations which correspond to holonomic $\\mathcal{D}$-modules on $\\mathbb{CP}^1$ with at most 2 regular singularities. We construct further examples with more singularities and develop a computer program for the computation of this correspondence in more general cases.","url_abs":"https://arxiv.org/abs/2111.14774v2","url_pdf":"https://arxiv.org/pdf/2111.14774v2.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":"an-investigation-into-lie-algebra","repo_url":"https://github.com/julek99/dmodrep","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}