{"id":"https://openalex.org/W7214733856","doi":"https://doi.org/10.48550/arxiv.2609.32916","title":"Well-tempered symmetric spaces","display_name":"Well-tempered symmetric spaces","publication_year":2026,"publication_date":"2026-09-26","ids":{"openalex":"https://openalex.org/W7214733856","doi":"https://doi.org/10.48550/arxiv.2609.32916"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.32916","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32916","pdf_url":"https://arxiv.org/pdf/2609.32916","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/2609.32916","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043892588","display_name":"Alexandre Afgoustidis","orcid":"https://orcid.org/0000-0002-6580-7951","observed_orcids":["https://orcid.org/0000-0002-6580-7951"]},"institutions":[{"id":"https://openalex.org/I204465549","display_name":"Washington University in St. Louis","ror":"https://ror.org/01yc7t268","country_code":"US","type":"education","lineage":["https://openalex.org/I204465549"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Afgoustidis, Alexandre","raw_affiliation_strings":["DEPARTMENT OF MATHEMATICS , WASHINGTON UNIVERSITY , ST. LOUIS , MO , 63130 , UNITED STATES"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DEPARTMENT OF MATHEMATICS , WASHINGTON UNIVERSITY , ST. LOUIS , MO , 63130 , UNITED STATES","institution_ids":["https://openalex.org/I204465549"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049195995","display_name":"Peter Hochs","orcid":"https://orcid.org/0000-0001-9232-2936","observed_orcids":["https://orcid.org/0000-0001-9232-2936"]},"institutions":[{"id":"https://openalex.org/I204465549","display_name":"Washington University in St. Louis","ror":"https://ror.org/01yc7t268","country_code":"US","type":"education","lineage":["https://openalex.org/I204465549"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hochs, Peter","raw_affiliation_strings":["DEPARTMENT OF MATHEMATICS , WASHINGTON UNIVERSITY , ST. LOUIS , MO , 63130 , UNITED STATES"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DEPARTMENT OF MATHEMATICS , WASHINGTON UNIVERSITY , ST. LOUIS , MO , 63130 , UNITED STATES","institution_ids":["https://openalex.org/I204465549"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088522032","display_name":"Shintaro Nishikawa","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I204465549","display_name":"Washington University in St. Louis","ror":"https://ror.org/01yc7t268","country_code":"US","type":"education","lineage":["https://openalex.org/I204465549"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nishikawa, Shintaro","raw_affiliation_strings":["DEPARTMENT OF MATHEMATICS , WASHINGTON UNIVERSITY , ST. LOUIS , MO , 63130 , UNITED STATES"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DEPARTMENT OF MATHEMATICS , WASHINGTON UNIVERSITY , ST. LOUIS , MO , 63130 , UNITED STATES","institution_ids":["https://openalex.org/I204465549"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5153411886","display_name":"Yanli Song","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I204465549","display_name":"Washington University in St. Louis","ror":"https://ror.org/01yc7t268","country_code":"US","type":"education","lineage":["https://openalex.org/I204465549"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Song, Yanli","raw_affiliation_strings":["DEPARTMENT OF MATHEMATICS , WASHINGTON UNIVERSITY , ST. LOUIS , MO , 63130 , UNITED STATES"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DEPARTMENT OF MATHEMATICS , WASHINGTON UNIVERSITY , ST. LOUIS , MO , 63130 , UNITED STATES","institution_ids":["https://openalex.org/I204465549"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I204465549"],"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":0.9951000213623047,"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":0.9951000213623047,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.004600000102072954,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/plancherel-measure","display_name":"Plancherel measure","score":0.9300000071525574},{"id":"https://openalex.org/keywords/fell-topology","display_name":"Fell topology","score":0.7680000066757202},{"id":"https://openalex.org/keywords/tempered-representations","display_name":"tempered representations","score":0.6579999923706055},{"id":"https://openalex.org/keywords/cartan-subgroup","display_name":"Cartan subgroup","score":0.6420000195503235},{"id":"https://openalex.org/keywords/weyl-group","display_name":"Weyl group","score":0.9559999704360962},{"id":"https://openalex.org/keywords/k-theory","display_name":"K-theory","score":0.9179999828338623},{"id":"https://openalex.org/keywords/discrete-spectrum","display_name":"discrete spectrum","score":0.38999998569488525}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8791000247001648},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5766000151634216},{"id":"https://openalex.org/C109385661","wikidata":"https://www.wikidata.org/wiki/Q11358307","display_name":"Triple system","level":2,"score":0.48989999294281006},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4377000033855438},{"id":"https://openalex.org/C139941754","wikidata":"https://www.wikidata.org/wiki/Q3058244","display_name":"Symmetric space","level":2,"score":0.41620001196861267},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.40470001101493835},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.4043999910354614},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.40380001068115234},{"id":"https://openalex.org/C75174853","wikidata":"https://www.wikidata.org/wiki/Q190629","display_name":"Centralizer and normalizer","level":2,"score":0.4025999903678894},{"id":"https://openalex.org/C197273675","wikidata":"https://www.wikidata.org/wiki/Q13220368","display_name":"Representation theory","level":2,"score":0.3968000113964081},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.3824999928474426},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.36880001425743103},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.35519999265670776},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.35409998893737793},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3483999967575073},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.31690001487731934},{"id":"https://openalex.org/C130133044","wikidata":"https://www.wikidata.org/wiki/Q1887083","display_name":"Compact group","level":3,"score":0.3131999969482422},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.31189998984336853},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.3019999861717224},{"id":"https://openalex.org/C31498916","wikidata":"https://www.wikidata.org/wiki/Q583034","display_name":"Locally compact space","level":2,"score":0.30160000920295715},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.3001999855041504},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.29840001463890076},{"id":"https://openalex.org/C171322552","wikidata":"https://www.wikidata.org/wiki/Q3427423","display_name":"Induced representation","level":3,"score":0.2842999994754791},{"id":"https://openalex.org/C2776122010","wikidata":"https://www.wikidata.org/wiki/Q10359539","display_name":"Unitary representation","level":3,"score":0.28380000591278076},{"id":"https://openalex.org/C54506234","wikidata":"https://www.wikidata.org/wiki/Q7314231","display_name":"Representation theory of the symmetric group","level":3,"score":0.2831999957561493},{"id":"https://openalex.org/C85307737","wikidata":"https://www.wikidata.org/wiki/Q751969","display_name":"Coset","level":2,"score":0.27950000762939453},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2759000062942505},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.2750000059604645},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.27149999141693115},{"id":"https://openalex.org/C89436406","wikidata":"https://www.wikidata.org/wiki/Q1544261","display_name":"Totally disconnected space","level":3,"score":0.26190000772476196},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.25690001249313354},{"id":"https://openalex.org/C2777044963","wikidata":"https://www.wikidata.org/wiki/Q5384707","display_name":"Equivalence class (music)","level":2,"score":0.25600001215934753},{"id":"https://openalex.org/C2776038885","wikidata":"https://www.wikidata.org/wiki/Q1555242","display_name":"Regular representation","level":3,"score":0.2535000145435333},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.25130000710487366}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.32916","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32916","pdf_url":"https://arxiv.org/pdf/2609.32916","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.2609.32916","doi":"https://doi.org/10.48550/arxiv.2609.32916","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.32916","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.32916","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32916","pdf_url":"https://arxiv.org/pdf/2609.32916","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":[{"id":"https://openalex.org/G2234892590","display_name":"Symmetry and analytic torsion","funder_award_id":"OCENW.M.21.176","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G4307962506","display_name":"FRG: Collaborative Research: The Hypoelliptic Laplacian, Noncommutative Geometry, and Applications to Representations and Singular Spaces","funder_award_id":"1952557","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6297983914","display_name":"Operator algebras and representation theory of Lie groups and groupoids","funder_award_id":"ANR-23-CE40-0016","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7080048889","display_name":null,"funder_award_id":"ANR-23","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7600566726","display_name":"Higher invariants of finite-volume spaces","funder_award_id":"OCENW.M.23.063","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G913291176","display_name":null,"funder_award_id":"OCENW.M.21","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214733856.pdf","grobid_xml":"https://content.openalex.org/works/W7214733856.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4391631520"],"related_works":["https://openalex.org/W1995980420","https://openalex.org/W1520847722","https://openalex.org/W1981712888","https://openalex.org/W7098053153","https://openalex.org/W1973921288","https://openalex.org/W4403663715","https://openalex.org/W231231489","https://openalex.org/W4299989504","https://openalex.org/W2952733655","https://openalex.org/W1975847057"],"abstract_inverted_index":{"Let":[0],"$X=G/H$":[1],"be":[2],"a":[3,49,73,96,130,163,168,176],"real":[4,76,169],"reductive":[5],"symmetric":[6,62,77,141],"space.":[7],"We":[8,28,64],"consider":[9],"the":[10,13,17,32,52,57,86,92,102,114,124,133,136,154,158,172,194,198],"support":[11,53,134,173],"of":[12,20,40,51,56,60,75,105,116,126,132,135,145,147,150,157,178,181,201],"Plancherel":[14,33,137],"measure":[15,138],"for":[16,35,72,139],"regular":[18,199],"representation":[19,200],"$G$":[21,106,161,202],"on":[22,123,203],"$L^2(X)$,":[23,204],"and":[24,42,118,152,166,205],"its":[25,206],"Fell":[26,155],"topology.":[27],"first":[29],"recall":[30],"how":[31],"formula":[34],"$X$":[36,79],"(known":[37],"from":[38],"work":[39],"Delorme":[41],"van":[43],"den":[44],"Ban--Schlicktrull,":[45],"among":[46],"others)":[47],"yields":[48],"description":[50,70,131],"in":[54,101,113,143],"terms":[55,144],"discrete":[58],"spectra":[59],"smaller":[61],"spaces.":[63],"then":[65,171],"point":[66],"out":[67],"that":[68],"this":[69],"simplifies":[71],"class":[74],"spaces":[78,87,110,142,184],"which":[80],"we":[81,128,192],"call":[82],"well-tempered.":[83],"These":[84],"are":[85,111],"whose":[88,99],"tangent":[89],"space":[90],"at":[91],"identity":[93],"coset":[94],"admits":[95],"Cartan":[97,148],"subspace":[98],"centralizer":[100],"Lie":[103],"algebra":[104],"is":[107,162],"abelian.":[108],"Well-tempered":[109],"tempered":[112],"sense":[115],"Benoist":[117],"Kobayashi.":[119],"Under":[120],"mild":[121],"assumptions":[122],"disconnectedness":[125],"$G$,":[127,151],"give":[129],"well-tempered":[140],"characters":[146],"subgroups":[149],"describe":[153,193],"topology":[156],"support.":[159],"If":[160],"complex":[164],"group":[165],"$H$":[167],"form,":[170],"decomposes":[174],"as":[175],"union":[177],"explicit":[179],"quotients":[180],"relative":[182],"continuous-parameter":[183],"by":[185],"finite":[186],"Weyl":[187],"groups.":[188],"As":[189],"an":[190],"application,":[191],"$C^*$-algebra":[195],"associated":[196],"to":[197],"$K$-theory.":[207]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}
