{"id":"https://openalex.org/W7220416689","doi":"https://doi.org/10.48550/arxiv.2610.02547","title":"Uniform Computability of Isotypic Block Diagonalization for Finite-Group Representations","display_name":"Uniform Computability of Isotypic Block Diagonalization for Finite-Group Representations","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7220416689","doi":"https://doi.org/10.48550/arxiv.2610.02547"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.02547","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02547","pdf_url":"https://arxiv.org/pdf/2610.02547","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/2610.02547","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024409727","display_name":"Konrad Burnik","orcid":"https://orcid.org/0000-0002-4406-4167","observed_orcids":["https://orcid.org/0000-0002-4406-4167"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Burnik, Konrad","raw_affiliation_strings":["CCA 2026 , Trier , Germany. Independent researcher , Amsterdam , the Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CCA 2026 , Trier , Germany. Independent researcher , Amsterdam , the Netherlands","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5024409727"],"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.8363999724388123,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.8363999724388123,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.03849999979138374,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.012500000186264515,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/representation-theory-of-finite-groups","display_name":"representation theory of finite groups","score":0.9580000042915344},{"id":"https://openalex.org/keywords/centralizers","display_name":"centralizers","score":0.8209999799728394},{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.9440000057220459},{"id":"https://openalex.org/keywords/wedderburn-decomposition","display_name":"Wedderburn decomposition","score":0.9190000295639038},{"id":"https://openalex.org/keywords/orthogonal-representations","display_name":"orthogonal representations","score":0.7390000224113464}],"concepts":[{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.6927000284194946},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.684499979019165},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6718000173568726},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.570900022983551},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5254999995231628},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44040000438690186},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39239999651908875},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3596000075340271},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.35260000824928284},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34470000863075256},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.34049999713897705},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3246000111103058},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3111000061035156},{"id":"https://openalex.org/C2983050975","wikidata":"https://www.wikidata.org/wiki/Q88287214","display_name":"Block structure","level":3,"score":0.2842999994754791},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.27480000257492065},{"id":"https://openalex.org/C2776230367","wikidata":"https://www.wikidata.org/wiki/Q7314222","display_name":"Representation theorem","level":2,"score":0.2685000002384186},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25679999589920044}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.02547","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02547","pdf_url":"https://arxiv.org/pdf/2610.02547","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.2610.02547","doi":"https://doi.org/10.48550/arxiv.2610.02547","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.02547","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.02547","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02547","pdf_url":"https://arxiv.org/pdf/2610.02547","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/W7220416689.pdf","grobid_xml":"https://content.openalex.org/works/W7220416689.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W877743272","https://openalex.org/W1979080577","https://openalex.org/W1997145001","https://openalex.org/W2015590395","https://openalex.org/W2024123675","https://openalex.org/W2025267089","https://openalex.org/W2033819630","https://openalex.org/W2042956211","https://openalex.org/W2080180423","https://openalex.org/W2145911343","https://openalex.org/W2810212916","https://openalex.org/W7164023646"],"related_works":["https://openalex.org/W47413800","https://openalex.org/W201011443","https://openalex.org/W7118053357","https://openalex.org/W2225440852","https://openalex.org/W234330441","https://openalex.org/W2022958494","https://openalex.org/W3105809659","https://openalex.org/W2954863491","https://openalex.org/W3195033085","https://openalex.org/W2189608787"],"abstract_inverted_index":{"We":[0,14],"study":[1],"the":[2,8,21,36,48,55,80,87],"universal":[3,22],"isotypic":[4,49],"block-diagonalization":[5],"problem":[6],"in":[7,47],"Type-2":[9],"theory":[10],"of":[11,27],"effectivity":[12],"(TTE).":[13],"obtain":[15],"a":[16,60,76],"uniform":[17],"computability":[18],"result":[19],"for":[20,25],"block":[23],"diagonalizer":[24],"commutants":[26],"given":[28,37,75],"finite":[29],"group":[30],"representations.":[31],"As":[32],"an":[33],"application,":[34],"when":[35],"representation":[38],"is":[39,65,69],"orthogonal,":[40],"we":[41],"compute":[42],"ordinary":[43],"$QR$":[44],"factorizations":[45],"blockwise":[46],"basis.":[50],"After":[51],"transforming":[52],"back":[53],"to":[54],"original":[56],"coordinates":[57],"this":[58],"yields":[59],"factorization":[61],"$A=QX$,":[62],"where":[63],"$Q$":[64],"orthogonal":[66,78],"and":[67],"$X$":[68],"generally":[70],"not":[71],"upper":[72],"triangular.":[73],"Moreover,":[74],"Wedderburn-adapted":[77],"basis,":[79],"transformed-back":[81],"factors":[82],"can":[83],"be":[84],"computed":[85],"within":[86],"commutant.":[88]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-06T00:00:00"}