{"id":"https://openalex.org/W7212040301","doi":"https://doi.org/10.48550/arxiv.2609.08024","title":"Atomic Decompositions of Lie Characters and the Dominant Weight Poset","display_name":"Atomic Decompositions of Lie Characters and the Dominant Weight Poset","publication_year":2026,"publication_date":"2026-09-07","ids":{"openalex":"https://openalex.org/W7212040301","doi":"https://doi.org/10.48550/arxiv.2609.08024"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.08024","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.08024","pdf_url":"https://arxiv.org/pdf/2609.08024","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/2609.08024","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5150945848","display_name":"Felipe de Mattos Chafik Hindi","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hindi, Felipe de Mattos Chafik","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5020387800","display_name":"Waldeck Sch\u00fctzer","orcid":"https://orcid.org/0000-0001-9098-2519","observed_orcids":["https://orcid.org/0000-0001-9098-2519"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Schutzer, Waldeck","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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.7782999873161316,"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":0.7782999873161316,"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":0.12710000574588776,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.07180000096559525,"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/atomic-number","display_name":"atomic number","score":0.7369999885559082},{"id":"https://openalex.org/keywords/semisimple-lie-algebras","display_name":"semisimple Lie algebras","score":0.8410000205039978},{"id":"https://openalex.org/keywords/irreducible-representations","display_name":"irreducible representations","score":0.6129999756813049},{"id":"https://openalex.org/keywords/weight-multiplicities","display_name":"weight multiplicities","score":0.6119999885559082},{"id":"https://openalex.org/keywords/mobius-transform","display_name":"M\u00f6bius transform","score":0.8029999732971191},{"id":"https://openalex.org/keywords/dynkin-diagrams","display_name":"Dynkin diagrams","score":0.8629999756813049},{"id":"https://openalex.org/keywords/kostant-partition-function","display_name":"Kostant partition function","score":0.8360000252723694},{"id":"https://openalex.org/keywords/raising-and-lowering-operators","display_name":"raising and lowering operators","score":0.7490000128746033},{"id":"https://openalex.org/keywords/type-g2","display_name":"type G2","score":0.8870000243186951}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9014999866485596},{"id":"https://openalex.org/C114411622","wikidata":"https://www.wikidata.org/wiki/Q5319218","display_name":"Dynkin diagram","level":3,"score":0.6692000031471252},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6032000184059143},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.588100016117096},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.5800999999046326},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5540000200271606},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5281999707221985},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.46399998664855957},{"id":"https://openalex.org/C142292226","wikidata":"https://www.wikidata.org/wiki/Q13690522","display_name":"Irreducible representation","level":2,"score":0.4542999863624573},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.43549999594688416},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.41179999709129333},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38440001010894775},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34929999709129333},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3206000030040741},{"id":"https://openalex.org/C134466208","wikidata":"https://www.wikidata.org/wiki/Q1520657","display_name":"Weight function","level":2,"score":0.2842999994754791},{"id":"https://openalex.org/C2778052762","wikidata":"https://www.wikidata.org/wiki/Q2366896","display_name":"Semisimple Lie algebra","level":5,"score":0.28290000557899475},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C40233952","wikidata":"https://www.wikidata.org/wiki/Q768074","display_name":"Weyl group","level":2,"score":0.26460000872612},{"id":"https://openalex.org/C140002607","wikidata":"https://www.wikidata.org/wiki/Q901446","display_name":"Hasse diagram","level":3,"score":0.25119999051094055}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.08024","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.08024","pdf_url":"https://arxiv.org/pdf/2609.08024","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.2609.08024","doi":"https://doi.org/10.48550/arxiv.2609.08024","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.08024","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:2609.08024","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.08024","pdf_url":"https://arxiv.org/pdf/2609.08024","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212040301.pdf","grobid_xml":"https://content.openalex.org/works/W7212040301.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4417006868","https://openalex.org/W7202157441"],"related_works":["https://openalex.org/W2890000735","https://openalex.org/W2021564172","https://openalex.org/W2791879042","https://openalex.org/W2187431034","https://openalex.org/W2963995819","https://openalex.org/W3021672100","https://openalex.org/W2995889621","https://openalex.org/W3131876536","https://openalex.org/W389011514","https://openalex.org/W4387540284"],"abstract_inverted_index":{"Let":[0],"$\\mathfrak{g}$":[1],"be":[2,17],"a":[3,10,32,110,201,221],"complex":[4],"semisimple":[5],"Lie":[6],"algebra":[7],"and,":[8],"for":[9,166,248],"dominant":[11,51,168,234],"integral":[12],"weight":[13,122],"$\u03bb$,":[14],"let":[15],"$\u0398_\u03bb$":[16],"the":[18,22,25,35,43,61,65,69,73,90,106,114,117,148,153,189,233,242,249],"multiplicity-free":[19],"sum":[20,80],"of":[21,24,34,64,81,89,92,105,119,128,134,139,191,246],"weights":[23],"irreducible":[26,198,206],"module":[27],"$V(\u03bb)$.":[28],"The":[29],"$\u0398_\u03bc$":[30],"form":[31],"$\\mathbb{Z}$-basis":[33],"$W$-invariants,":[36],"so":[37],"there":[38],"are":[39,57,60,256],"unique":[40],"integers":[41],"$a(\u03bc,\u03bb)$,":[42],"atomic":[44,212,254],"numbers,":[45],"with":[46,116,170,200],"$\\mathrm{ch}\\,V(\u03bb)":[47],"=":[48,172,182],"\\sum_\u03bca(\u03bc,\u03bb)\u0398_\u03bc$":[49],"over":[50],"$\u03bc$.":[52],"We":[53,96],"ask":[54],"when":[55,216],"they":[56],"nonnegative.":[58],"They":[59],"Moebius":[62],"transform":[63],"weight-multiplicity":[66],"function":[67],"on":[68],"dominant-weight":[70],"poset,":[71],"which":[72],"crosscut":[74],"theorem":[75],"turns":[76],"into":[77,196],"an":[78,120,205,237],"alternating":[79],"at":[82],"most":[83],"$2^{\\mathrm{rank}\\,\u03a6}$":[84],"multiplicities":[85],"indexed":[86],"by":[87,130],"subsets":[88],"covers":[91],"$\u03bc$":[93,169],"in":[94,145,224,232,236],"$[\u03bc,\u03bb]$.":[95],"prove":[97],"that":[98],"$a(\u03bc,\u03bb)\\ge":[99],"0$":[100,183],"whenever":[101],"every":[102,167,197],"connected":[103],"component":[104],"Dynkin":[107,218],"diagram":[108,219],"is":[109,125,155,178,220,241],"path,":[111,222],"and":[112,137,174,184],"identify":[113],"coefficient":[115],"dimension":[118],"explicit":[121,238],"space:":[123],"it":[124],"cut":[126],"out":[127],"$V(\u03bb)$":[129],"alternately":[131],"taking":[132],"kernels":[133],"raising":[135],"operators":[136],"cokernels":[138],"lowering":[140],"operators,":[141],"one":[142],"per":[143],"cover,":[144],"order":[146],"along":[147],"path.":[149],"Type":[150],"$D_4$":[151],"shows":[152],"hypothesis":[154],"necessary.":[156],"Put":[157],"$\u03b2=":[158],"\u03b1_1":[159],"+":[160,162,164],"2\u03b1_2":[161],"2\u03b1_3":[163],"2\u03b1_4$;":[165],"$\\langle\u03bc,\u03b1_2^\\vee\\rangle":[171],"1$":[173],"$\u03bc+\u03b2$":[175],"dominant,":[176],"$a(\u03bc,\u03bc+\u03b2)$":[177],"$-2$":[179],"if":[180],"$\\langle\u03bc,\u03b1_1^\\vee\\rangle":[181],"$-1$":[185],"otherwise.":[186],"Restriction":[187],"to":[188,259],"support":[190],"$\u03bb-\u03bc$":[192,247],"carries":[193],"this":[194],"family":[195],"type":[199],"trivalent":[202],"node.":[203],"Thus":[204],"finite":[207],"root":[208],"system":[209],"has":[210],"all":[211],"numbers":[213,255],"nonnegative":[214],"exactly":[215],"its":[217],"namely":[223],"types":[225],"$A_n$,":[226],"$B_n$,":[227],"$C_n$,":[228],"$F_4$,":[229],"$G_2$.":[230],"Deep":[231],"chamber,":[235],"range,":[239],"$a(\u03bc,\u03bb)$":[240],"Kostant":[243],"partition":[244],"number":[245],"nonsimple":[250],"positive":[251],"roots;":[252],"negative":[253],"therefore":[257],"confined":[258],"boundary":[260],"slabs.":[261]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-10T00:00:00"}
