{"id":"https://openalex.org/W7224122129","doi":"https://doi.org/10.48550/arxiv.2610.37184","title":"Representations of shifted quantum affine algebras and cluster algebras II: Non simply-laced types and cluster expansions","display_name":"Representations of shifted quantum affine algebras and cluster algebras II: Non simply-laced types and cluster expansions","publication_year":2026,"publication_date":"2026-10-27","ids":{"openalex":"https://openalex.org/W7224122129","doi":"https://doi.org/10.48550/arxiv.2610.37184"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.37184","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.37184","pdf_url":"https://arxiv.org/pdf/2610.37184","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/2610.37184","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076889629","display_name":"Christof Gei\u00df","orcid":"https://orcid.org/0000-0002-8196-7541","observed_orcids":["https://orcid.org/0000-0002-8196-7541"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Geiss, Christof","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102796273","display_name":"David Hernandez","orcid":"https://orcid.org/0000-0003-1822-1488","observed_orcids":["https://orcid.org/0000-0003-1822-1488"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hernandez, David","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5110929350","display_name":"Bernard Leclerc","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Leclerc, Bernard","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9990000128746033,"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":0.9990000128746033,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.0003000000142492354,"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/T11680","display_name":"Advanced Algebra and Geometry","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/cluster-algebras","display_name":"cluster algebras","score":0.9679999947547913},{"id":"https://openalex.org/keywords/grothendieck-ring","display_name":"Grothendieck ring","score":0.765999972820282},{"id":"https://openalex.org/keywords/category-o","display_name":"category O","score":0.7080000042915344},{"id":"https://openalex.org/keywords/cluster-monomials","display_name":"cluster monomials","score":0.878000020980835},{"id":"https://openalex.org/keywords/cluster-expansion","display_name":"cluster expansion","score":0.7789999842643738},{"id":"https://openalex.org/keywords/positivity","display_name":"positivity","score":0.7020000219345093},{"id":"https://openalex.org/keywords/formal-power-series","display_name":"formal power series","score":0.7739999890327454}],"concepts":[{"id":"https://openalex.org/C165879259","wikidata":"https://www.wikidata.org/wiki/Q5136690","display_name":"Cluster algebra","level":3,"score":0.7602999806404114},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7287999987602234},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.6571000218391418},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.6301000118255615},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.558899998664856},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5547999739646912},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5070000290870667},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.48260000348091125},{"id":"https://openalex.org/C187999345","wikidata":"https://www.wikidata.org/wiki/Q7269007","display_name":"Quantum affine algebra","level":5,"score":0.42480000853538513},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.40880000591278076},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3589000105857849},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35260000824928284},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.33649998903274536},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.31850001215934753},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3111000061035156},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.28790000081062317},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.2833999991416931},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.26179999113082886}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.37184","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.37184","pdf_url":"https://arxiv.org/pdf/2610.37184","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.2610.37184","doi":"https://doi.org/10.48550/arxiv.2610.37184","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.37184","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:2610.37184","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.37184","pdf_url":"https://arxiv.org/pdf/2610.37184","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":[{"id":"https://openalex.org/F4320335100","display_name":"Direcci\u00f3n General de Asuntos del Personal Acad\u00e9mico, Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":"https://ror.org/01tmp8f25"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224122129.pdf","grobid_xml":"https://content.openalex.org/works/W7224122129.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4401658396","https://openalex.org/W2057769404","https://openalex.org/W248380103","https://openalex.org/W2990584981","https://openalex.org/W4406959986","https://openalex.org/W4415348654","https://openalex.org/W2912935737","https://openalex.org/W2935952278","https://openalex.org/W4287608704","https://openalex.org/W2405247007"],"abstract_inverted_index":{"We":[0,25],"extend":[1],"our":[2],"previous":[3],"results":[4],"on":[5],"cluster":[6,39,55],"structures":[7],"in":[8,41],"the":[9,21,32,38],"Grothendieck":[10],"rings":[11],"of":[12,37,43,45,54],"categories":[13],"$\\mathcal{O}^{\\mathrm{sh}}$":[14],"for":[15,29],"shifted":[16],"quantum":[17],"affine":[18],"algebras":[19],"to":[20],"non-simply":[22],"laced":[23],"types.":[24],"also":[26],"show":[27],"that,":[28],"all":[30],"types,":[31],"formal":[33],"power":[34],"series":[35],"expressions":[36],"monomials":[40],"terms":[42],"classes":[44],"positive":[46],"prefundamental":[47],"representations":[48],"can":[49],"be":[50],"regarded":[51],"as":[52],"limits":[53],"expansions,":[56],"thus":[57],"establishing":[58],"their":[59],"positivity.":[60]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-29T00:00:00"}
