{"id":"https://openalex.org/W7208748655","doi":"https://doi.org/10.48550/arxiv.2609.03882","title":"Additive diameters and covering complexity of irreducible representations","display_name":"Additive diameters and covering complexity of irreducible representations","publication_year":2026,"publication_date":"2026-09-03","ids":{"openalex":"https://openalex.org/W7208748655","doi":"https://doi.org/10.48550/arxiv.2609.03882"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.03882","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.03882","pdf_url":"https://arxiv.org/pdf/2609.03882","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/2609.03882","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033391512","display_name":"Urban Jezernik","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jezernik, Urban","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5047928240","display_name":"\u0160pela \u0160penko","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"\u0160penko, \u0160pela","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":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/T10849","display_name":"Finite Group Theory Research","score":0.9193999767303467,"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/T10849","display_name":"Finite Group Theory Research","score":0.9193999767303467,"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":0.07519999891519547,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.0026000000070780516,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/irreducible-representations","display_name":"irreducible representations","score":0.9620000123977661},{"id":"https://openalex.org/keywords/compact-galaxy-groups","display_name":"compact groups","score":0.5820000171661377},{"id":"https://openalex.org/keywords/linear-group-actions","display_name":"linear group actions","score":0.6980000138282776},{"id":"https://openalex.org/keywords/sl-2-c","display_name":"SL(2,C)","score":0.6000000238418579},{"id":"https://openalex.org/keywords/symmetric-powers","display_name":"symmetric powers","score":0.6890000104904175},{"id":"https://openalex.org/keywords/exterior-powers","display_name":"exterior powers","score":0.996999979019165},{"id":"https://openalex.org/keywords/heisenberg-group","display_name":"Heisenberg group","score":0.8159999847412109},{"id":"https://openalex.org/keywords/reductive-groups","display_name":"reductive groups","score":0.828000009059906},{"id":"https://openalex.org/keywords/flag-varieties","display_name":"flag varieties","score":0.8190000057220459},{"id":"https://openalex.org/keywords/finite-heisenberg-group","display_name":"finite Heisenberg group","score":0.5139999985694885}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.866100013256073},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5605000257492065},{"id":"https://openalex.org/C142292226","wikidata":"https://www.wikidata.org/wiki/Q13690522","display_name":"Irreducible representation","level":2,"score":0.5587999820709229},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5098000168800354},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4851999878883362},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4634999930858612},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.45509999990463257},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4456000030040741},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.42329999804496765},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.4104999899864197},{"id":"https://openalex.org/C195592935","wikidata":"https://www.wikidata.org/wiki/Q4544947","display_name":"(g,K)-module","level":5,"score":0.400299996137619},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3885999917984009},{"id":"https://openalex.org/C2776730729","wikidata":"https://www.wikidata.org/wiki/Q1392130","display_name":"Flag (linear algebra)","level":3,"score":0.38839998841285706},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.37529999017715454},{"id":"https://openalex.org/C197273675","wikidata":"https://www.wikidata.org/wiki/Q13220368","display_name":"Representation theory","level":2,"score":0.37450000643730164},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.37139999866485596},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.36719998717308044},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.36550000309944153},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3424000144004822},{"id":"https://openalex.org/C127519595","wikidata":"https://www.wikidata.org/wiki/Q1601337","display_name":"Heisenberg group","level":2,"score":0.3278000056743622},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.3246000111103058},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.32030001282691956},{"id":"https://openalex.org/C2776122010","wikidata":"https://www.wikidata.org/wiki/Q10359539","display_name":"Unitary representation","level":3,"score":0.31790000200271606},{"id":"https://openalex.org/C179415260","wikidata":"https://www.wikidata.org/wiki/Q1006450","display_name":"Reductive group","level":3,"score":0.31439998745918274},{"id":"https://openalex.org/C158464096","wikidata":"https://www.wikidata.org/wiki/Q7314224","display_name":"Representation theory of SU","level":5,"score":0.3077999949455261},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.30730000138282776},{"id":"https://openalex.org/C81651864","wikidata":"https://www.wikidata.org/wiki/Q874429","display_name":"Group theory","level":2,"score":0.27950000762939453},{"id":"https://openalex.org/C2776823524","wikidata":"https://www.wikidata.org/wiki/Q6073561","display_name":"Irreducibility","level":2,"score":0.2750000059604645},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.27059999108314514},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.26820001006126404},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.2671999931335449},{"id":"https://openalex.org/C5106717","wikidata":"https://www.wikidata.org/wiki/Q3427416","display_name":"Fundamental representation","level":4,"score":0.262800008058548},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.25690001249313354},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.250900000333786}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.03882","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.03882","pdf_url":"https://arxiv.org/pdf/2609.03882","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.2609.03882","doi":"https://doi.org/10.48550/arxiv.2609.03882","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.03882","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:2609.03882","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.03882","pdf_url":"https://arxiv.org/pdf/2609.03882","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/G3344805299","display_name":"Rapid random generation of Lie algebras","funder_award_id":"J1-50001","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"},{"id":"https://openalex.org/G6502505638","display_name":"Algebra, operator theory and financial mathematics","funder_award_id":"P1-0222","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"},{"id":"https://openalex.org/G8870577881","display_name":"Random matrices, graphs, and groups","funder_award_id":"J1-70033","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"}],"funders":[{"id":"https://openalex.org/F4320321390","display_name":"Fonds De La Recherche Scientifique - FNRS","ror":"https://ror.org/03q83t159"},{"id":"https://openalex.org/F4320322554","display_name":"Javna Agencija za Raziskovalno Dejavnost RS","ror":"https://ror.org/059bp8k51"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7208748655.pdf","grobid_xml":"https://content.openalex.org/works/W7208748655.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W6910701558","https://openalex.org/W7134834359"],"related_works":["https://openalex.org/W6910701558","https://openalex.org/W7212024540","https://openalex.org/W1483941506","https://openalex.org/W2041259548","https://openalex.org/W4283362994","https://openalex.org/W7095354254","https://openalex.org/W3128675458","https://openalex.org/W2068502516","https://openalex.org/W4246214144","https://openalex.org/W2047602923"],"abstract_inverted_index":{"Let":[0],"a":[1,7,17,85,182,208,244],"group":[2,206],"$G$":[3,51],"act":[4],"linearly":[5],"on":[6,184,191,232],"finite-dimensional":[8],"complex":[9],"vector":[10],"space":[11],"$V$.":[12,35],"The":[13,141,176],"group-additive":[14],"diameter":[15,59,102,237,255],"of":[16,26,28,34,60,103,135,149,154,170,188,196,210,221],"subspace":[18,63,105],"$U":[19],"\\leq":[20,114,116,247],"V$":[21],"is":[22,32,39,52,56,64,81,161,178,249,256],"the":[23,58,78,90,93,97,101,185,192,199,219,222,227,235,252],"least":[24,41,218],"number":[25],"translates":[27],"$U$":[29],"whose":[30,213],"sum":[31],"all":[33],"Counting":[36],"dimensions,":[37],"it":[38,160],"at":[40,65,217],"$\\dim":[42],"V":[43,69,75],"/":[44,70],"\\dim":[45,71,74,120],"U$.":[46],"We":[47,88],"show":[48],"that":[49,112],"when":[50],"compact":[53],"and":[54,106,122,151,159,167,190],"$V$":[55],"irreducible,":[57],"every":[61,202],"nonzero":[62],"most":[66],"$\\lceil":[67],"(\\dim":[68],"U)":[72],"\\ln":[73,119],"\\rceil$,":[76],"so":[77,111],"trivial":[79,108],"bound":[80],"correct":[82],"up":[83],"to":[84,216,240],"logarithmic":[86],"factor.":[87],"measure":[89],"discrepancy":[91],"by":[92,181],"covering":[94],"complexity":[95,177],"$\\mathsf{C}(V)$,":[96],"largest":[98],"ratio":[99],"between":[100],"any":[104],"its":[107],"lower":[109],"bound,":[110],"$1":[113],"\\mathsf{C}(V)":[115],"2":[117],"+":[118],"V$,":[121],"we":[123],"determine":[124],"where":[125],"in":[126],"this":[127],"range":[128],"various":[129],"representations":[130,187,193,212],"lie.":[131],"Every":[132],"irreducible":[133,211],"representation":[134],"$\\mathrm{SL}_2(\\mathbf{C})$":[136],"has":[137,207],"$\\mathsf{C}(V)":[138],"=":[139],"1$.":[140],"logarithm":[142],"can":[143],"be":[144],"genuinely":[145],"present":[146,162],"along":[147],"families":[148],"symmetric":[150],"exterior":[152],"powers":[153],"$\\mathrm{SL}_n(\\mathbf{C})$":[155,189],"with":[156,238],"$n$":[157],"varying,":[158],"for":[163,226,243],"finite":[164],"Heisenberg":[165],"groups":[166,169],"$2$-transitive":[168],"small":[171],"order":[172],"such":[173],"as":[174],"$\\mathrm{PSL}_2(\\mathbf{F}_p)$.":[175],"bounded":[179],"above":[180],"constant":[183],"conjugation":[186],"$\\operatorname{Sym}^k":[194,233,241],"\\mathbf{C}^3$":[195,248],"$\\mathrm{SL}_3(\\mathbf{C})$.":[197],"On":[198],"other":[200],"hand,":[201],"fixed":[203],"connected":[204],"reductive":[205],"family":[209],"complexities":[214],"tend":[215],"dimension":[220],"flag":[223],"variety.":[224],"Finally,":[225],"Lie":[228],"algebra":[229],"$\\mathfrak{sl}_3(\\mathbf{C})$":[230],"acting":[231],"\\mathbf{C}^3$,":[234],"monomial":[236],"respect":[239],"X$":[242],"plane":[245],"$X":[246],"optimal,":[250],"while":[251],"corresponding":[253],"$\\mathrm{SL}_3(\\mathbf{C})$":[254],"not.":[257]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-05T00:00:00"}
