{"id":"https://openalex.org/W7225574369","doi":"https://doi.org/10.5281/zenodo.24058776","title":"Invariant Measures and Volumes on SU(N) and its Complex Projective Cosets A Fully Analytic Treatment","display_name":"Invariant Measures and Volumes on SU(N) and its Complex Projective Cosets A Fully Analytic Treatment","publication_year":2026,"publication_date":"2026-11-08","ids":{"openalex":"https://openalex.org/W7225574369","doi":"https://doi.org/10.5281/zenodo.24058776"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24058776","doi":"https://doi.org/10.5281/zenodo.24058776","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24058776","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24058776","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058003244","display_name":"Stefano Bertini","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Bertini, Stefano","raw_affiliation_strings":["Politecnico di Milano"],"raw_orcid":"https://orcid.org/0009-0002-1620-0480","affiliations":[{"raw_affiliation_string":"Politecnico di Milano","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5058003244"],"corresponding_institution_ids":["https://openalex.org/I93860229"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.7026000022888184,"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":0.7026000022888184,"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/T12504","display_name":"Mathematics and Applications","score":0.061000000685453415,"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"}},{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.02449999935925007,"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/haar-measure","display_name":"Haar measure","score":0.8130000233650208},{"id":"https://openalex.org/keywords/invariant-measures","display_name":"invariant measures","score":0.7540000081062317},{"id":"https://openalex.org/keywords/complex-projective-space","display_name":"complex projective space","score":0.8140000104904175},{"id":"https://openalex.org/keywords/coset-spaces","display_name":"coset spaces","score":0.5809999704360962},{"id":"https://openalex.org/keywords/fibrations","display_name":"fibrations","score":0.6150000095367432},{"id":"https://openalex.org/keywords/jacobian-matrix","display_name":"Jacobian matrix","score":0.8769999742507935}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.798799991607666},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.6626999974250793},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6096000075340271},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5561000108718872},{"id":"https://openalex.org/C134949993","wikidata":"https://www.wikidata.org/wiki/Q2068617","display_name":"Pencil (optics)","level":2,"score":0.5213000178337097},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.49630001187324524},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.46320000290870667},{"id":"https://openalex.org/C54486226","wikidata":"https://www.wikidata.org/wiki/Q493941","display_name":"Fibration","level":3,"score":0.45500001311302185},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.41839998960494995},{"id":"https://openalex.org/C85307737","wikidata":"https://www.wikidata.org/wiki/Q751969","display_name":"Coset","level":2,"score":0.39820000529289246},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.3953000009059906},{"id":"https://openalex.org/C134315596","wikidata":"https://www.wikidata.org/wiki/Q7249475","display_name":"Projective unitary group","level":5,"score":0.382099986076355},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.375},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3610000014305115},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.2825999855995178},{"id":"https://openalex.org/C91229774","wikidata":"https://www.wikidata.org/wiki/Q193885","display_name":"Infinitesimal","level":2,"score":0.2750999927520752},{"id":"https://openalex.org/C75280867","wikidata":"https://www.wikidata.org/wiki/Q877775","display_name":"Projective space","level":3,"score":0.2624000012874603},{"id":"https://openalex.org/C115667082","wikidata":"https://www.wikidata.org/wiki/Q4200518","display_name":"Invariant measure","level":3,"score":0.2578999996185303},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2572999894618988},{"id":"https://openalex.org/C132702353","wikidata":"https://www.wikidata.org/wiki/Q2538404","display_name":"Complex projective space","level":4,"score":0.25429999828338623}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24058776","doi":"https://doi.org/10.5281/zenodo.24058776","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24058776","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},{"id":"doi:10.5281/zenodo.24058777","doi":"https://doi.org/10.5281/zenodo.24058777","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24058777","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"doi:10.5281/zenodo.24058776","doi":"https://doi.org/10.5281/zenodo.24058776","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24058776","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1614484218","https://openalex.org/W1984730732","https://openalex.org/W2094812845","https://openalex.org/W7225423743","https://openalex.org/W2114755007","https://openalex.org/W1757619019","https://openalex.org/W6912019293","https://openalex.org/W2043898387","https://openalex.org/W2161703163","https://openalex.org/W1980167301"],"abstract_inverted_index":{"A":[0],"fully":[1],"analytic":[2],"treatment":[3],"of":[4,33,42,57,60,72],"the":[5,12,28,31,40,43,45,48,51,55,61,69,79],"invariant":[6],"(Haar)":[7],"measures":[8],"and":[9,17,30,50,59,78],"volumes":[10],"on":[11,18],"special":[13],"unitary":[14],"groups":[15],"SU(N)":[16,58],"their":[19],"complex":[20],"projective":[21,62],"cosets.":[22],"The":[23,64],"measure":[24],"is":[25,85],"constructed":[26],"from":[27],"fibration":[29],"cascade":[32],"odd":[34],"spheres,":[35],"with":[36,68],"every":[37],"step":[38],"displayed:":[39],"Jacobian":[41],"parametrisation,":[44],"recursion":[46],"for":[47,54],"measure,":[49],"closed":[52],"form":[53],"volume":[56,84],"quotients.":[63],"results":[65],"are":[66,87],"compared":[67],"classical":[70],"formulas":[71],"Marinov,":[73],"including":[74],"his":[75],"published":[76],"correction,":[77],"conventions":[80],"under":[81],"which":[82],"each":[83],"quoted":[86],"stated":[88],"explicitly.":[89]},"counts_by_year":[],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2026-11-09T00:00:00"}
