{"id":"https://openalex.org/W7204459562","doi":"https://doi.org/10.48550/arxiv.2608.25651","title":"Stable Symmetric Series, Differential Operators, and Jack Deformations","display_name":"Stable Symmetric Series, Differential Operators, and Jack Deformations","publication_year":2026,"publication_date":"2026-08-26","ids":{"openalex":"https://openalex.org/W7204459562","doi":"https://doi.org/10.48550/arxiv.2608.25651"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.25651","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.25651","pdf_url":"https://arxiv.org/pdf/2608.25651","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/2608.25651","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085392129","display_name":"Jean\u2010Yves Thibon","orcid":"https://orcid.org/0000-0002-8976-4044","observed_orcids":["https://orcid.org/0000-0002-8976-4044"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Thibon, Jean-Yves","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5085392129"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9897000193595886,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9897000193595886,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.0017999999690800905,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.0015999999595806003,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/symmetric-group","display_name":"symmetric group","score":0.7039999961853027},{"id":"https://openalex.org/keywords/jack-polynomials","display_name":"Jack polynomials","score":0.7509999871253967},{"id":"https://openalex.org/keywords/differential-operators","display_name":"differential operators","score":0.7710000276565552},{"id":"https://openalex.org/keywords/weyl-algebra","display_name":"Weyl algebra","score":0.6119999885559082},{"id":"https://openalex.org/keywords/zonal-polynomials","display_name":"zonal polynomials","score":0.8529999852180481},{"id":"https://openalex.org/keywords/conjugacy-classes","display_name":"conjugacy classes","score":0.7639999985694885},{"id":"https://openalex.org/keywords/multiplication-operators","display_name":"multiplication operators","score":0.3709999918937683}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.774399995803833},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.6133000254631042},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5928999781608582},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.5367000102996826},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.529699981212616},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4706000089645386},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.45680001378059387},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4496000111103058},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4309000074863434},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.39959999918937683},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39100000262260437},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.36469998955726624},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36039999127388},{"id":"https://openalex.org/C35958075","wikidata":"https://www.wikidata.org/wiki/Q1425077","display_name":"Spectral theorem","level":3,"score":0.3230000138282776},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3188000023365021},{"id":"https://openalex.org/C87945829","wikidata":"https://www.wikidata.org/wiki/Q1353233","display_name":"Conjugacy class","level":2,"score":0.31679999828338623},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.3122999966144562},{"id":"https://openalex.org/C191832335","wikidata":"https://www.wikidata.org/wiki/Q4262191","display_name":"Fourier integral operator","level":3,"score":0.2992999851703644},{"id":"https://openalex.org/C41106240","wikidata":"https://www.wikidata.org/wiki/Q526790","display_name":"Skew-symmetric matrix","level":5,"score":0.2957000136375427},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2946000099182129},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.2797999978065491},{"id":"https://openalex.org/C129683796","wikidata":"https://www.wikidata.org/wiki/Q430450","display_name":"Microlocal analysis","level":4,"score":0.27160000801086426},{"id":"https://openalex.org/C129010115","wikidata":"https://www.wikidata.org/wiki/Q1298683","display_name":"Power sum symmetric polynomial","level":5,"score":0.26919999718666077},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.2612999975681305},{"id":"https://openalex.org/C103275481","wikidata":"https://www.wikidata.org/wiki/Q6787889","display_name":"Matrix representation","level":3,"score":0.2605000138282776},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.25999999046325684},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.25920000672340393},{"id":"https://openalex.org/C186080144","wikidata":"https://www.wikidata.org/wiki/Q358733","display_name":"Series expansion","level":2,"score":0.2587999999523163},{"id":"https://openalex.org/C54506234","wikidata":"https://www.wikidata.org/wiki/Q7314231","display_name":"Representation theory of the symmetric group","level":3,"score":0.25519999861717224}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.25651","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.25651","pdf_url":"https://arxiv.org/pdf/2608.25651","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.2608.25651","doi":"https://doi.org/10.48550/arxiv.2608.25651","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.25651","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:2608.25651","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.25651","pdf_url":"https://arxiv.org/pdf/2608.25651","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/W7204459562.pdf","grobid_xml":"https://content.openalex.org/works/W7204459562.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W2996090912"],"related_works":["https://openalex.org/W7204944487","https://openalex.org/W2006238822","https://openalex.org/W1734969601","https://openalex.org/W2001439135","https://openalex.org/W4298853425","https://openalex.org/W2057990722","https://openalex.org/W2886095825","https://openalex.org/W647208150","https://openalex.org/W2006698464","https://openalex.org/W7100194884"],"abstract_inverted_index":{"We":[0],"introduce":[1],"stable":[2],"symmetric":[3,17,30],"series":[4],"which":[5],"encode":[6],"normalized":[7],"conjugacy":[8],"classes":[9],"and":[10,32,54,57,65,69,81],"their":[11],"multiplication":[12],"operators":[13,35,61],"simultaneously":[14],"for":[15],"all":[16],"groups.":[18],"This":[19],"gives":[20],"a":[21],"direct":[22],"route":[23],"from":[24],"the":[25,40,45],"Ivanov--Kerov":[26],"algebra":[27],"to":[28,33,47,72],"shifted":[29,51],"functions":[31],"differential":[34],"in":[36,62],"$U(\\mathcal":[37],"W_{1+\\infty})$.":[38],"Using":[39],"Goulden--Jackson":[41],"product,":[42],"we":[43],"extend":[44],"construction":[46],"Jack":[48,52],"polynomials,":[49],"recover":[50],"eigenvalues":[53],"Pieri-type":[55],"relations,":[56],"obtain":[58],"explicit":[59],"candidate":[60],"degrees":[63],"three":[64],"four.":[66],"Their":[67],"real":[68],"quaternionic":[70],"specializations":[71],"zonal":[73],"polynomials":[74],"are":[75],"verified":[76],"by":[77],"Gaussian":[78],"matrix":[79],"integrals":[80],"exhaustive":[82],"Wick":[83],"enumeration.":[84]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-28T00:00:00"}