{"id":"https://openalex.org/W7203662386","doi":"https://doi.org/10.48550/arxiv.2608.16800","title":"Characterization of $\\mathfrak{k}$-highest weight and $\\widehat{\\mathfrak{g}}$-dominant tableaux via $1$-$0$-slack recording tableaux in the quantum Littlewood-Richardson rule and lattice points in flagged hive polytopes","display_name":"Characterization of $\\mathfrak{k}$-highest weight and $\\widehat{\\mathfrak{g}}$-dominant tableaux via $1$-$0$-slack recording tableaux in the quantum Littlewood-Richardson rule and lattice points in flagged hive polytopes","publication_year":2026,"publication_date":"2026-08-17","ids":{"openalex":"https://openalex.org/W7203662386","doi":"https://doi.org/10.48550/arxiv.2608.16800"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.16800","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.16800","pdf_url":"https://arxiv.org/pdf/2608.16800","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":"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/2608.16800","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057861201","display_name":"Olga Azenhas","orcid":"https://orcid.org/0000-0001-7718-7158","observed_orcids":["https://orcid.org/0000-0001-7718-7158"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Azenhas, Olga","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5057861201"],"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":0.9994999766349792,"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":0.9994999766349792,"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":9.999999747378752e-05,"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":0.0,"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/lattice-points","display_name":"lattice points","score":0.8640000224113464},{"id":"https://openalex.org/keywords/linear-inequalities","display_name":"linear inequalities","score":0.6520000100135803},{"id":"https://openalex.org/keywords/young-tableaux","display_name":"Young tableaux","score":0.5339999794960022},{"id":"https://openalex.org/keywords/affine-kac-moody-algebras","display_name":"affine Kac-Moody algebras","score":0.7480000257492065}],"concepts":[{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.9857000112533569},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.9527000188827515},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.6481000185012817},{"id":"https://openalex.org/C165368118","wikidata":"https://www.wikidata.org/wiki/Q2166280","display_name":"Young tableau","level":2,"score":0.6395999789237976},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6126999855041504},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5911999940872192},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5317000150680542},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38519999384880066},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.361299991607666},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3434999883174896},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.3425999879837036},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.33329999446868896},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3133000135421753},{"id":"https://openalex.org/C2776608160","wikidata":"https://www.wikidata.org/wiki/Q4785462","display_name":"Natural (archaeology)","level":2,"score":0.28999999165534973},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.2614000141620636},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.2531999945640564}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.16800","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.16800","pdf_url":"https://arxiv.org/pdf/2608.16800","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.16800","doi":"https://doi.org/10.48550/arxiv.2608.16800","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.16800","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:2608.16800","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.16800","pdf_url":"https://arxiv.org/pdf/2608.16800","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3204329492","display_name":null,"funder_award_id":"UID/PRR/00324/2025","funder_id":"https://openalex.org/F4320335246","funder_display_name":"Centro de Matem\u00e1tica, Universidade de Coimbra"},{"id":"https://openalex.org/G3431946983","display_name":"Centro de Matem\u00e1tica da Universidade de Coimbra","funder_award_id":"UID/00324/2025","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G5712257541","display_name":null,"funder_award_id":"UID/00324/2025","funder_id":"https://openalex.org/F4320335246","funder_display_name":"Centro de Matem\u00e1tica, Universidade de Coimbra"},{"id":"https://openalex.org/G6265307419","display_name":null,"funder_award_id":"UID/00324","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G6997658380","display_name":null,"funder_award_id":"10.54499","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G7126425900","display_name":"Centro de Matem\u00e1tica da Universidade de Coimbra","funder_award_id":"UID/PRR/00324/2025","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G8985288032","display_name":null,"funder_award_id":"UID/00324","funder_id":"https://openalex.org/F4320335246","funder_display_name":"Centro de Matem\u00e1tica, Universidade de Coimbra"}],"funders":[{"id":"https://openalex.org/F4320323392","display_name":"Universidade de Coimbra","ror":"https://ror.org/04z8k9a98"},{"id":"https://openalex.org/F4320334779","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","ror":"https://ror.org/00snfqn58"},{"id":"https://openalex.org/F4320335246","display_name":"Centro de Matem\u00e1tica, Universidade de Coimbra","ror":"https://ror.org/04z8k9a98"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203662386.pdf","grobid_xml":"https://content.openalex.org/works/W7203662386.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W4410974074","https://openalex.org/W4416046378","https://openalex.org/W7123648465","https://openalex.org/W7138923786","https://openalex.org/W7158323378","https://openalex.org/W7165801824"],"related_works":["https://openalex.org/W7138923786","https://openalex.org/W7158323378","https://openalex.org/W2297385013","https://openalex.org/W7203462595","https://openalex.org/W2033569189","https://openalex.org/W2049514700","https://openalex.org/W2964279988","https://openalex.org/W6923731976","https://openalex.org/W2136682184","https://openalex.org/W4292107122"],"abstract_inverted_index":{"We":[0,36],"have":[1],"previously,":[2],"for":[3,41,110,144],"a":[4,162],"given":[5,87],"positive":[6],"integer":[7],"$n$,":[8],"explicitly":[9,65],"characterized":[10,106],"by":[11,26,67,107],"certain":[12,68],"linear":[13,69,108],"inequalities":[14,70,109],"the":[15,31,47,53,71,76,86,94,98,118,135,145,158],"$\\mathfrak{k}$-highest":[16,57,95,152],"weight":[17,58,96,153],"tableaux":[18,29,59,74,100,104,116,156],"of":[19,49,165],"shape":[20,43,77,112],"length":[21,78],"$2n$":[22,80],"or":[23,81,91],"$2n-1$":[24],"produced":[25],"$1$-$0$-slack":[27,102],"recording":[28,103,115],"in":[30,117,123,161],"quantum":[32,119,137],"Littlewood-Richardson":[33,120],"(LR)":[34],"rule.":[35],"now":[37],"extend":[38],"that":[39],"characterization":[40],"lower":[42,111],"lengths.":[44,113],"Then":[45],"using":[46],"composition":[48],"promotion":[50],"operators":[51],"defining":[52],"Naito-Suzuki-Watanabe":[54],"bijection":[55,125],"between":[56,151],"and":[60,97,148,157],"$\\widehat{\\mathfrak{g}}$-dominant":[61,73,99,155],"tableaux,":[62,129,154],"we":[63,130],"also":[64],"characterize":[66],"corresponding":[72],"when":[75,85],"is":[79,89],"$2n-1$.":[82],"In":[83],"addition,":[84],"$n$":[88],"$3$":[90],"$":[92],"4$":[93],"via":[101],"are":[105,122],"Since":[114],"rule":[121,139],"natural":[124],"with":[126,140],"Littlewood-Richardson-Sundaram":[127],"(LRS)":[128],"relate":[131],"our":[132],"results":[133],"on":[134],"inverse":[136],"LR":[138],"other":[141],"two":[142],"bijections":[143,150],"Naito-Sagaki":[146],"conjecture":[147],"establish":[149],"lattice":[159],"points":[160],"(disjoint)":[163],"union":[164],"flagged":[166],"hive":[167],"polytopes.":[168]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-08-19T00:00:00"}