{"id":"https://openalex.org/W1493123414","doi":"https://doi.org/10.37236/438","title":"Invariant and Coinvariant Spaces for the Algebra of Symmetric Polynomials in Non-Commuting Variables","display_name":"Invariant and Coinvariant Spaces for the Algebra of Symmetric Polynomials in Non-Commuting Variables","publication_year":2010,"publication_date":"2010-12-10","ids":{"openalex":"https://openalex.org/W1493123414","doi":"https://doi.org/10.37236/438","mag":"1493123414"},"language":"fr","primary_location":{"id":"doi:10.37236/438","is_oa":true,"landing_page_url":"https://doi.org/10.37236/438","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r166/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r166/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022387958","display_name":"Fran\u00e7ois Bergeron","orcid":"https://orcid.org/0000-0003-4566-6351"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fran\u00e7ois Bergeron","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5087494593","display_name":"Aaron Lauve","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Aaron Lauve","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04611628,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"1","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":0.24400000274181366,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.24400000274181366,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.23960000276565552,"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":0.08569999784231186,"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/combinatorics","display_name":"Combinatorics","score":0.7126625776290894},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6509655714035034},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.5583352446556091},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5075737237930298},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.4545135498046875},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36010438203811646},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2239377498626709},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.21518579125404358},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15250644087791443}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7126625776290894},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6509655714035034},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.5583352446556091},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5075737237930298},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.4545135498046875},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36010438203811646},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2239377498626709},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.21518579125404358},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15250644087791443}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/438","is_oa":true,"landing_page_url":"https://doi.org/10.37236/438","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r166/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/438","is_oa":true,"landing_page_url":"https://doi.org/10.37236/438","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r166/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321747","display_name":"Fonds Qu\u00e9b\u00e9cois de la Recherche sur la Nature et les Technologies","ror":"https://ror.org/00b9f9778"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1493123414.pdf","grobid_xml":"https://content.openalex.org/works/W1493123414.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W639181740","https://openalex.org/W1528326162","https://openalex.org/W1551679380","https://openalex.org/W1569820464","https://openalex.org/W1983373140","https://openalex.org/W1992551970","https://openalex.org/W1997444728","https://openalex.org/W2019582080","https://openalex.org/W2031777414","https://openalex.org/W2032758875","https://openalex.org/W2044877038","https://openalex.org/W2047602652","https://openalex.org/W2072178019","https://openalex.org/W2074762481","https://openalex.org/W2079173352","https://openalex.org/W2112736257","https://openalex.org/W2118886915","https://openalex.org/W2126209209","https://openalex.org/W2134984950","https://openalex.org/W2963446937","https://openalex.org/W3101730715"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W2594491092","https://openalex.org/W2963288955","https://openalex.org/W2368341314","https://openalex.org/W2601315865","https://openalex.org/W2320266418","https://openalex.org/W1441003567","https://openalex.org/W4249642042","https://openalex.org/W1978539514","https://openalex.org/W1999572366"],"abstract_inverted_index":{"We":[0,46],"analyze":[1],"the":[2,5,26,29,37,40,44,56],"structure":[3,70,90],"of":[4,8,28,52,59],"algebra":[6],"$\\mathbb{K}\\langle\\mathbf{x}\\rangle^{\\mathfrak{S}_n}$":[7,53,73,123],"symmetric":[9,30],"polynomials":[10,42],"in":[11,14],"non-commuting":[12],"variables":[13,79,99],"so":[15],"far":[16],"as":[17,39],"it":[18],"relates":[19],"to":[20,35,55],"$\\mathbb{K}[\\mathbf{x}]^{\\mathfrak{S}_n}$,":[21],"its":[22],"commutative":[23],"counterpart.":[24],"Using":[25],"\"place-action\"":[27],"group,":[31],"we":[32],"are":[33],"able":[34],"realize":[36],"latter":[38],"invariant":[41],"inside":[43],"former.":[45],"discover":[47],"a":[48],"tensor":[49],"product":[50],"decomposition":[51],"analogous":[54],"classical":[57],"theorems":[58],"Chevalley,":[60],"Shephard-Todd":[61],"on":[62,109],"finite":[63],"reflection":[64],"groups.":[65],"R\u00e9sum\u00e9.":[66],"Nous":[67],"analysons":[68],"la":[69,89],"de":[71,91,105,114,122,134],"l'alg\u00e8bre":[72],"des":[74,78,83,85,94,98,131],"polyn\u00f4mes":[75,95],"sym\u00e9triques":[76,96],"en":[77,97],"non-commutatives":[80],"pour":[81],"obtenir":[82],"analogues":[84,130],"r\u00e9sultats":[86],"classiques":[87,133],"concernant":[88],"l'anneau":[92],"$\\mathbb{K}[\\mathbf{x}]^{\\mathfrak{S}_n}$":[93,111],"commutatives.":[100],"Plus":[101],"pr\u00e9cis\u00e9ment,":[102],"au":[103],"moyen":[104],"\"l'action":[106],"par":[107],"positions\",":[108],"r\u00e9alise":[110],"comme":[112,124],"sous-module":[113],"$\\mathbb{K}\\langle\\mathbf{x}\\rangle^{\\mathfrak{S}_n}$.":[115],"On":[116],"d\u00e9couvre":[117],"alors":[118],"une":[119],"nouvelle":[120],"d\u00e9composition":[121],"produit":[125],"tensorial,":[126],"obtenant":[127],"ainsi":[128],"un":[129],"th\u00e9or\u00e8mes":[132],"Chevalley":[135],"et":[136],"Shephard-Todd.":[137]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
