{"id":"https://openalex.org/W7214714497","doi":"https://doi.org/10.48550/arxiv.2609.35393","title":"Jordan induction for $\\mathrm{GL}_n(\\mathcal{O})$","display_name":"Jordan induction for $\\mathrm{GL}_n(\\mathcal{O})$","publication_year":2026,"publication_date":"2026-09-28","ids":{"openalex":"https://openalex.org/W7214714497","doi":"https://doi.org/10.48550/arxiv.2609.35393"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.35393","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.35393","pdf_url":"https://arxiv.org/pdf/2609.35393","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.35393","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153413678","display_name":"Zhe Chen","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chen, Zhe","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5153413678"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/smooth-representations","display_name":"smooth representations","score":0.8519999980926514},{"id":"https://openalex.org/keywords/nilpotent-orbits","display_name":"nilpotent orbits","score":0.8579999804496765},{"id":"https://openalex.org/keywords/irreducible-representations","display_name":"irreducible representations","score":0.8799999952316284},{"id":"https://openalex.org/keywords/discrete-valuation-rings","display_name":"discrete valuation rings","score":0.5979999899864197},{"id":"https://openalex.org/keywords/finite-residue-field","display_name":"finite residue field","score":0.781000018119812}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7488999962806702},{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.7067999839782715},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.5867999792098999},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5443999767303467},{"id":"https://openalex.org/C2779873844","wikidata":"https://www.wikidata.org/wiki/Q986694","display_name":"Discrete valuation ring","level":2,"score":0.47209998965263367},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4530999958515167},{"id":"https://openalex.org/C147073270","wikidata":"https://www.wikidata.org/wiki/Q567083","display_name":"Annihilator","level":3,"score":0.4059999883174896},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3910999894142151},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.3698999881744385},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.3578000068664551},{"id":"https://openalex.org/C2779462738","wikidata":"https://www.wikidata.org/wiki/Q17146409","display_name":"Realisation","level":2,"score":0.3409999907016754},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30379998683929443},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.30329999327659607},{"id":"https://openalex.org/C2781025942","wikidata":"https://www.wikidata.org/wiki/Q7315530","display_name":"Residue field","level":3,"score":0.2944999933242798},{"id":"https://openalex.org/C142292226","wikidata":"https://www.wikidata.org/wiki/Q13690522","display_name":"Irreducible representation","level":2,"score":0.2921000123023987},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.287200003862381},{"id":"https://openalex.org/C144558754","wikidata":"https://www.wikidata.org/wiki/Q5282068","display_name":"Discrete valuation","level":3,"score":0.26260000467300415}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.35393","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.35393","pdf_url":"https://arxiv.org/pdf/2609.35393","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.35393","doi":"https://doi.org/10.48550/arxiv.2609.35393","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.35393","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.35393","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.35393","pdf_url":"https://arxiv.org/pdf/2609.35393","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214714497.pdf","grobid_xml":"https://content.openalex.org/works/W7214714497.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W4396652683","https://openalex.org/W4402426767","https://openalex.org/W4416131875","https://openalex.org/W7077918524"],"related_works":["https://openalex.org/W1995869869","https://openalex.org/W2171086100","https://openalex.org/W7153953898","https://openalex.org/W1965827771","https://openalex.org/W1580161966","https://openalex.org/W77127219","https://openalex.org/W912076416","https://openalex.org/W2952245360","https://openalex.org/W4294436465","https://openalex.org/W7220926741"],"abstract_inverted_index":{"Let":[0],"$\\mathcal{O}$":[1],"be":[2],"a":[3,9,15,79,88,103],"complete":[4],"discrete":[5],"valuation":[6],"ring":[7],"with":[8,122],"finite":[10],"residue":[11],"field.":[12],"We":[13,100],"introduce":[14],"simple":[16,89],"framework":[17],"of":[18,22,27,69,72,82],"constructing":[19],"smooth":[20],"representations":[21],"$\\mathrm{GL}_n(\\mathcal{O})$":[23],"modulo":[24],"the":[25,46,60,97,114],"knowledge":[26],"nilpotent":[28],"orbits,":[29],"called":[30],"Jordan":[31,74,106],"induction,":[32,110],"which":[33],"enjoys":[34],"several":[35],"remarkable":[36],"properties:":[37],"It":[38],"yields":[39,44,56],"only":[40],"irreducible":[41,49],"representations,":[42,50],"it":[43,55],"all":[45],"even":[47,61],"level":[48,62],"and":[51,108],"up":[52],"to":[53,96],"conjugation":[54],"non-isomorphic":[57],"representations.":[58],"In":[59],"case,":[63],"this":[64],"gives":[65],"an":[66,93],"explicit":[67,94],"realisation":[68],"Hill's":[70],"analogue":[71],"Lusztig's":[73],"decomposition,":[75],"as":[76,78],"well":[77],"vast":[80],"generalisation":[81],"G\u00e9rardin's":[83],"construction":[84],"for":[85],"$\\mathrm{GL}_n(\\mathcal{O})$.":[86],"As":[87],"application,":[90],"we":[91],"construct":[92],"section":[95],"orbit":[98],"map.":[99],"also":[101],"propose":[102],"conjecture":[104],"linking":[105],"induction":[107],"Lusztig":[109],"aiming":[111],"at":[112],"generalising":[113],"algebraisation":[115],"theorem":[116],"obtained":[117],"in":[118],"recent":[119],"joint":[120],"works":[121],"Stasinski.":[123]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}
