{"id":"https://openalex.org/W2952425502","doi":"https://doi.org/10.48550/arxiv.math/0308281","title":"Quantum Groups at Roots of Unity and Modularity","display_name":"Quantum Groups at Roots of Unity and Modularity","publication_year":2003,"publication_date":"2003-08-28","ids":{"openalex":"https://openalex.org/W2952425502","doi":"https://doi.org/10.48550/arxiv.math/0308281","mag":"2952425502"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:math/0308281","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0308281","pdf_url":"https://arxiv.org/pdf/math/0308281","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/math/0308281","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007242685","display_name":"Stephen Sawin","orcid":"https://orcid.org/0000-0001-9218-4780","observed_orcids":["https://orcid.org/0000-0001-9218-4780"]},"institutions":[{"id":"https://openalex.org/I126350171","display_name":"Fairfield University","ror":"https://ror.org/04z49n283","country_code":"US","type":"education","lineage":["https://openalex.org/I126350171"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Sawin, Stephen F.","raw_affiliation_strings":["Department of Math. and C. S., Fairfield University, Fairfield, CT, 06824-5195, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Math. and C. S., Fairfield University, Fairfield, CT, 06824-5195, USA","institution_ids":["https://openalex.org/I126350171"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5007242685"],"corresponding_institution_ids":["https://openalex.org/I126350171"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9976000189781189,"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"}},"topics":[{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9976000189781189,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.00039999998989515007,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.0003000000142492354,"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/quantum-groups-at-roots-of-unity","display_name":"quantum groups at roots of unity","score":0.9440000057220459},{"id":"https://openalex.org/keywords/modular-tensor-categories","display_name":"modular tensor categories","score":0.9890000224113464},{"id":"https://openalex.org/keywords/modularity","display_name":"modularity","score":0.6639999747276306},{"id":"https://openalex.org/keywords/compact-simple-lie-groups","display_name":"compact simple Lie groups","score":0.7020000219345093},{"id":"https://openalex.org/keywords/tensor-product-decomposition","display_name":"tensor product decomposition","score":0.828000009059906},{"id":"https://openalex.org/keywords/representation-theory-of-quantum-groups","display_name":"representation theory of quantum groups","score":0.7210000157356262},{"id":"https://openalex.org/keywords/simply-connected-lie-groups","display_name":"simply connected Lie groups","score":0.6470000147819519}],"concepts":[{"id":"https://openalex.org/C206343339","wikidata":"https://www.wikidata.org/wiki/Q756747","display_name":"Root of unity","level":3,"score":0.7896555066108704},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7869202494621277},{"id":"https://openalex.org/C2780617661","wikidata":"https://www.wikidata.org/wiki/Q541563","display_name":"Subcategory","level":2,"score":0.7165392637252808},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6657440066337585},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.6094165444374084},{"id":"https://openalex.org/C197273675","wikidata":"https://www.wikidata.org/wiki/Q13220368","display_name":"Representation theory","level":2,"score":0.5216784477233887},{"id":"https://openalex.org/C2779478453","wikidata":"https://www.wikidata.org/wiki/Q6889748","display_name":"Modularity (biology)","level":2,"score":0.5053884983062744},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.48208123445510864},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4749752879142761},{"id":"https://openalex.org/C119494637","wikidata":"https://www.wikidata.org/wiki/Q7249476","display_name":"Projective representation","level":3,"score":0.47361254692077637},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.473576158285141},{"id":"https://openalex.org/C75764964","wikidata":"https://www.wikidata.org/wiki/Q870797","display_name":"Modular form","level":2,"score":0.4412469267845154},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.432896226644516},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4198809266090393},{"id":"https://openalex.org/C148647251","wikidata":"https://www.wikidata.org/wiki/Q2122223","display_name":"Quantum group","level":3,"score":0.4190233051776886},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.2585376501083374},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.12513038516044617},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09565383195877075},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:arXiv.org:math/0308281","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0308281","pdf_url":"https://arxiv.org/pdf/math/0308281","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":"mag:2952425502","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/math/0308281v2","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.763.208","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.763.208","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0308281.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.math/0308281","doi":"https://doi.org/10.48550/arxiv.math/0308281","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.math/0308281","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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:math/0308281","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0308281","pdf_url":"https://arxiv.org/pdf/math/0308281","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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1490053529","https://openalex.org/W1500084468","https://openalex.org/W1518388118","https://openalex.org/W1565930783","https://openalex.org/W1579486099","https://openalex.org/W1666120112","https://openalex.org/W1964400499","https://openalex.org/W1966028892","https://openalex.org/W1966591147","https://openalex.org/W1973368764","https://openalex.org/W1975171921","https://openalex.org/W1983060363","https://openalex.org/W1985759733","https://openalex.org/W2010837137","https://openalex.org/W2014771251","https://openalex.org/W2027004210","https://openalex.org/W2027044855","https://openalex.org/W2028903958","https://openalex.org/W2043949003","https://openalex.org/W2080743555","https://openalex.org/W2081085222","https://openalex.org/W2088353214","https://openalex.org/W2091253256","https://openalex.org/W2091919572","https://openalex.org/W2120207347","https://openalex.org/W2121239399","https://openalex.org/W2135186723","https://openalex.org/W2137459590","https://openalex.org/W2330101626","https://openalex.org/W2507031302"],"related_works":["https://openalex.org/W2016558425","https://openalex.org/W2119906742","https://openalex.org/W1580232935","https://openalex.org/W2964316157","https://openalex.org/W3177882801","https://openalex.org/W2951023315","https://openalex.org/W3046622420","https://openalex.org/W2025752530","https://openalex.org/W1983317044","https://openalex.org/W2323843011","https://openalex.org/W3101555130","https://openalex.org/W2775523269","https://openalex.org/W3097929662","https://openalex.org/W2290789975","https://openalex.org/W2008140469","https://openalex.org/W2950041449","https://openalex.org/W3101722878","https://openalex.org/W2964321718","https://openalex.org/W1985545718","https://openalex.org/W2125084722"],"abstract_inverted_index":{"For":[0],"each":[1,8],"compact,":[2],"simple,":[3],"simply-connected":[4],"Lie":[5],"group":[6],"and":[7],"integer":[9],"level":[10],"we":[11],"construct":[12],"a":[13,18,21,48],"modular":[14],"tensor":[15,60],"category":[16,26,42],"from":[17],"quotient":[19],"of":[20,24,27,29,51,58,71,76,97],"certain":[22],"subcategory":[23],"the":[25,30,40,52,56,59,67,94,98],"representations":[28],"corresponding":[31,41],"quantum":[32,49,72],"group.":[33,99],"We":[34,45],"determine":[35],"when":[36],"at":[37,74],"fractional":[38,89],"levels":[39,90],"is":[43],"modular.":[44],"also":[46],"give":[47],"version":[50],"Racah":[53],"formula":[54],"for":[55],"decomposition":[57],"product.":[61],"This":[62],"work":[63,84],"relies":[64],"on":[65],"developing":[66],"basic":[68],"representation":[69],"theory":[70],"groups":[73],"roots":[75],"unity,":[77],"including":[78],"Harish-Chandra's":[79],"Theorem.":[80],"It":[81],"generalizes":[82],"previous":[83],"which":[85],"applied":[86],"only":[87,92],"to":[88,93],"or":[91],"projective":[95],"form":[96]},"counts_by_year":[],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2025-10-10T00:00:00"}
