{"id":"https://openalex.org/W2082973088","doi":"https://doi.org/10.1145/1073884.1073889","title":"Signature of symmetric rational matrices and the unitary dual of lie groups","display_name":"Signature of symmetric rational matrices and the unitary dual of lie groups","publication_year":2005,"publication_date":"2005-07-24","ids":{"openalex":"https://openalex.org/W2082973088","doi":"https://doi.org/10.1145/1073884.1073889","mag":"2082973088"},"language":"en","primary_location":{"id":"doi:10.1145/1073884.1073889","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1073884.1073889","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101686146","display_name":"Jeffrey Adams","orcid":"https://orcid.org/0000-0002-5964-2310"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jeffrey Adams","raw_affiliation_strings":["University of Maryland, College Park, MD"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Maryland, College Park, MD","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057745748","display_name":"B. David Saunders","orcid":null},"institutions":[{"id":"https://openalex.org/I86501945","display_name":"University of Delaware","ror":"https://ror.org/01sbq1a82","country_code":"US","type":"education","lineage":["https://openalex.org/I86501945"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"B. David Saunders","raw_affiliation_strings":["University of Delaware, Newark, DE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Delaware, Newark, DE","institution_ids":["https://openalex.org/I86501945"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100519505","display_name":"Zhendong Wan","orcid":"https://orcid.org/0009-0006-2546-1294"},"institutions":[{"id":"https://openalex.org/I86501945","display_name":"University of Delaware","ror":"https://ror.org/01sbq1a82","country_code":"US","type":"education","lineage":["https://openalex.org/I86501945"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhendong Wan","raw_affiliation_strings":["University of Delaware, Newark, DE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Delaware, Newark, DE","institution_ids":["https://openalex.org/I86501945"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.963,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.85462555,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"13","last_page":"20"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9968000054359436,"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":0.9958999752998352,"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/unitary-state","display_name":"Unitary state","score":0.7156254649162292},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6942487955093384},{"id":"https://openalex.org/keywords/special-unitary-group","display_name":"Special unitary group","score":0.5881181955337524},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5834875106811523},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.545940637588501},{"id":"https://openalex.org/keywords/unitary-matrix","display_name":"Unitary matrix","score":0.5394319891929626},{"id":"https://openalex.org/keywords/unitary-group","display_name":"Unitary group","score":0.529535174369812},{"id":"https://openalex.org/keywords/signature","display_name":"Signature (topology)","score":0.5248439311981201},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5073482394218445},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4850172698497772},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.48236769437789917},{"id":"https://openalex.org/keywords/lie-group","display_name":"Lie group","score":0.48231959342956543},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.45033082365989685},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4228185713291168},{"id":"https://openalex.org/keywords/circular-ensemble","display_name":"Circular ensemble","score":0.41413113474845886},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.4131982624530792},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3708050549030304},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32592859864234924},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32001805305480957},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10492947697639465},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07495084404945374}],"concepts":[{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.7156254649162292},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6942487955093384},{"id":"https://openalex.org/C32955637","wikidata":"https://www.wikidata.org/wiki/Q684363","display_name":"Special unitary group","level":2,"score":0.5881181955337524},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5834875106811523},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.545940637588501},{"id":"https://openalex.org/C96214315","wikidata":"https://www.wikidata.org/wiki/Q727103","display_name":"Unitary matrix","level":3,"score":0.5394319891929626},{"id":"https://openalex.org/C99072794","wikidata":"https://www.wikidata.org/wiki/Q1500617","display_name":"Unitary group","level":3,"score":0.529535174369812},{"id":"https://openalex.org/C2779696439","wikidata":"https://www.wikidata.org/wiki/Q7512811","display_name":"Signature (topology)","level":2,"score":0.5248439311981201},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5073482394218445},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4850172698497772},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.48236769437789917},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.48231959342956543},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.45033082365989685},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4228185713291168},{"id":"https://openalex.org/C11902944","wikidata":"https://www.wikidata.org/wiki/Q5121662","display_name":"Circular ensemble","level":4,"score":0.41413113474845886},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4131982624530792},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3708050549030304},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32592859864234924},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32001805305480957},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10492947697639465},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07495084404945374},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1073884.1073889","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1073884.1073889","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1502124338","https://openalex.org/W1933621332","https://openalex.org/W1980856175","https://openalex.org/W2009190506","https://openalex.org/W2019291580","https://openalex.org/W2045295714","https://openalex.org/W2048685209","https://openalex.org/W2055455800","https://openalex.org/W2057186674","https://openalex.org/W2071483197","https://openalex.org/W2126157726","https://openalex.org/W2128978199","https://openalex.org/W2149623001","https://openalex.org/W2572527475","https://openalex.org/W2798909945","https://openalex.org/W2951594791","https://openalex.org/W4298120002","https://openalex.org/W6679103854","https://openalex.org/W6750968397"],"related_works":["https://openalex.org/W3102585750","https://openalex.org/W2677100893","https://openalex.org/W4288356826","https://openalex.org/W2184469044","https://openalex.org/W3168010615","https://openalex.org/W2090722158","https://openalex.org/W2978272868","https://openalex.org/W2040375332","https://openalex.org/W3099833096","https://openalex.org/W1982986111"],"abstract_inverted_index":{"A":[0],"key":[1],"step":[2],"in":[3],"the":[4,7,15,30,43,72,80,90],"computation":[5,81],"of":[6,10,27,29,45],"unitary":[8],"dual":[9],"a":[11,66,85],"Lie":[12],"group":[13,75],"is":[14,82],"determination":[16],"if":[17],"certain":[18],"rational":[19],"symmetric":[20,54],"matrices":[21],"are":[22],"positive":[23],"semi-definite.":[24],"The":[25],"size":[26],"some":[28],"computations":[31,38],"dictates":[32],"that":[33,79],"high":[34],"performance":[35,60],"integer":[36,53],"matrix":[37,55,68],"be":[39],"used.":[40],"We":[41,77],"explore":[42],"feasibility":[44],"this":[46],"approach":[47],"by":[48],"developing":[49],"three":[50],"algorithms":[51],"for":[52,89],"signature":[56],"and":[57,63],"studying":[58],"their":[59],"both":[61],"asymptotically":[62],"experimentally":[64],"on":[65],"particular":[67],"family":[69],"constructed":[70],"from":[71],"exceptional":[73],"Weyl":[74],"E8.":[76],"conclude":[78],"doable,":[83],"with":[84],"parallel":[86],"implementation":[87],"needed":[88],"largest":[91],"representations.":[92]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}