{"id":"https://openalex.org/W7223308390","doi":"https://doi.org/10.48550/arxiv.2610.31655","title":"Plabic promotions beyond cluster: quantum cluster structures and the dual canonical basis","display_name":"Plabic promotions beyond cluster: quantum cluster structures and the dual canonical basis","publication_year":2026,"publication_date":"2026-10-22","ids":{"openalex":"https://openalex.org/W7223308390","doi":"https://doi.org/10.48550/arxiv.2610.31655"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.31655","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.31655","pdf_url":"https://arxiv.org/pdf/2610.31655","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/2610.31655","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159355094","display_name":"Jian-Rong Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Li, Jian-Rong","raw_affiliation_strings":["Faculty of Mathematics , University of Seville , Calle Tarfia s/n , 41012 Seville , Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics , University of Seville , Calle Tarfia s/n , 41012 Seville , Spain","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5159368698","display_name":"Michael Oren Perlstein","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Perlstein, Michael Oren","raw_affiliation_strings":["Department of Mathematics , Weizmann Institute of Science ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Weizmann Institute of Science ,","institution_ids":["https://openalex.org/I53964585"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068997721","display_name":"Ran J. Tessler","orcid":"https://orcid.org/0000-0002-4763-6378","observed_orcids":["https://orcid.org/0000-0002-4763-6378"]},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Tessler, Ran J.","raw_affiliation_strings":["Department of Mathematics , Weizmann Institute of Science , Rehovot , Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Weizmann Institute of Science , Rehovot , Israel","institution_ids":["https://openalex.org/I53964585"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9833999872207642,"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":0.9833999872207642,"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":0.011599999852478504,"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":0.0005000000237487257,"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/dual-canonical-basis","display_name":"dual canonical basis","score":0.9279999732971191},{"id":"https://openalex.org/keywords/grassmannians","display_name":"Grassmannians","score":0.843999981880188},{"id":"https://openalex.org/keywords/intersection-numbers","display_name":"intersection numbers","score":0.5339999794960022},{"id":"https://openalex.org/keywords/cluster-algebras","display_name":"cluster algebras","score":0.6110000014305115}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7814000248908997},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.720300018787384},{"id":"https://openalex.org/C165879259","wikidata":"https://www.wikidata.org/wiki/Q5136690","display_name":"Cluster algebra","level":3,"score":0.5716000199317932},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5231000185012817},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4742000102996826},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4625000059604645},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4618000090122223},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4586000144481659},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.42399999499320984},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.421099990606308},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.4007999897003174},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.38119998574256897},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.34150001406669617},{"id":"https://openalex.org/C2778753846","wikidata":"https://www.wikidata.org/wiki/Q6554239","display_name":"Link (geometry)","level":2,"score":0.33660000562667847},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3292999863624573},{"id":"https://openalex.org/C2775956649","wikidata":"https://www.wikidata.org/wiki/Q1189744","display_name":"Pfaffian","level":2,"score":0.31540000438690186},{"id":"https://openalex.org/C204707403","wikidata":"https://www.wikidata.org/wiki/Q1152398","display_name":"Canonical form","level":2,"score":0.3043000102043152},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.287200003862381},{"id":"https://openalex.org/C54643580","wikidata":"https://www.wikidata.org/wiki/Q1005603","display_name":"Algebraic combinatorics","level":2,"score":0.27790001034736633},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.2727999985218048},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.272599995136261},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.271699994802475},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.26260000467300415}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.31655","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.31655","pdf_url":"https://arxiv.org/pdf/2610.31655","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.2610.31655","doi":"https://doi.org/10.48550/arxiv.2610.31655","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.31655","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:2610.31655","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.31655","pdf_url":"https://arxiv.org/pdf/2610.31655","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223308390.pdf","grobid_xml":"https://content.openalex.org/works/W7223308390.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W1672638072","https://openalex.org/W4226297057","https://openalex.org/W4388067837","https://openalex.org/W7125912923"],"related_works":["https://openalex.org/W7127121368","https://openalex.org/W2560336494","https://openalex.org/W3013003606","https://openalex.org/W4401336004","https://openalex.org/W4387579970","https://openalex.org/W2575365786","https://openalex.org/W2133404484","https://openalex.org/W3018940274","https://openalex.org/W2127793607","https://openalex.org/W4226297057"],"abstract_inverted_index":{"Plabic":[0],"tangles":[1,62,158],"define":[2,91],"geometric":[3],"promotion":[4,32],"maps":[5],"between":[6,13],"configurations":[7],"and,":[8],"after":[9],"choosing":[10],"a":[11,67,116,205],"lift,":[12],"Grassmannians.":[14],"The":[15],"main":[16],"conjecture":[17,54,150,206],"in":[18,42,77,119,196],"\\cite{Tangles}":[19],"is":[20,25,33],"that":[21,55,80,102,137,151,189],"when":[22],"the":[23,29,39,48,78,81,92,134,138,160],"tangle":[24],"dominant":[26,60,156],"and":[27,72,124,140,149,186],"solvable":[28,61,157,169],"induced":[30],"algebraic":[31],"cluster":[34,40,69,87,99],"quasi-homomorphism.":[35],"This":[36],"work":[37],"extends":[38],"perspective":[41],"two":[43],"directions.":[44],"First,":[45],"we":[46,90],"initiate":[47],"study":[49,181],"of":[50,94,171,183,191,199],"quantum":[51,141],"promotions.":[52],"We":[53,132,163,177],"all":[56,75,152],"promotions":[57,144,153,166],"defined":[58],"from":[59,155],"are":[63,98],"naturally":[64],"lifted":[65],"to":[66,84,109,115,180,187],"\\emph{quantum":[68],"quasi":[70,100],"homomorphism},":[71],"prove":[73,133],"for":[74],"cases":[76],"literature":[79],"were":[82],"shown":[83],"be":[85],"(classical)":[86],"quasi-homomorphisms.":[88],"Secondly,":[89],"notion":[93],"cluster-Lusztig":[95],"quasi-homomorphisms,":[96],"which":[97],"homomorphisms":[101],"take":[103],"Lustig's":[104],"dual":[105,110,200],"canonical":[106,111,201],"basis":[107,112,202],"elements":[108],"element,":[113],"up":[114],"Laurent":[117],"monomial":[118],"frozen":[120],"variables,":[121],"with":[122],"clearing":[123],"normalization":[125],"chosen":[126],"uniformly":[127],"on":[128],"each":[129],"content":[130],"component.":[131],"unexpected":[135],"result":[136],"classical":[139],"$m$-unary":[142],"star":[143],"fall":[145],"into":[146],"this":[147],"category,":[148],"coming":[154],"share":[159],"same":[161],"property.":[162],"then":[164],"consider":[165],"via":[167],"non":[168],"cores":[170],"intersection":[172],"number":[173],"higher":[174],"than":[175],"one.":[176],"use":[178],"it":[179],"facets":[182],"amplituhedron":[184],"cells,":[185],"show":[188],"some":[190],"them":[192],"do":[193],"not":[194],"lie":[195],"zero":[197],"loci":[198],"elements,":[203],"disproving":[204],"by":[207],"T.":[208],"Lam":[209],"\\cite{LamGP}.":[210]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-24T00:00:00"}
