{"id":"https://openalex.org/W3045266193","doi":"https://doi.org/10.1142/s0218196720500435","title":"Hilbert series associated to symplectic quotients by SU2","display_name":"Hilbert series associated to symplectic quotients by SU2","publication_year":2020,"publication_date":"2020-07-24","ids":{"openalex":"https://openalex.org/W3045266193","doi":"https://doi.org/10.1142/s0218196720500435","mag":"3045266193"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196720500435","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196720500435","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},"type":"article","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/A5065397503","display_name":"Hans-Christian Herbig","orcid":"https://orcid.org/0000-0003-2676-3340"},"institutions":[{"id":"https://openalex.org/I157394403","display_name":"Baylor University","ror":"https://ror.org/005781934","country_code":"US","type":"education","lineage":["https://openalex.org/I157394403"]},{"id":"https://openalex.org/I117979880","display_name":"Rhodes College","ror":"https://ror.org/049xfwy04","country_code":"US","type":"education","lineage":["https://openalex.org/I117979880"]},{"id":"https://openalex.org/I122140584","display_name":"Universidade Federal do Rio de Janeiro","ror":"https://ror.org/03490as77","country_code":"BR","type":"education","lineage":["https://openalex.org/I122140584"]}],"countries":["BR","US"],"is_corresponding":true,"raw_author_name":"Hans-Christian Herbig","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada, Universidade Federal do Rio de Janeiro, Avenedo Athos da Silveira Ramos 149, Centro de Tecnologia \u2014 Bloco C, CEP 21941-909 Rio de Janeiro, Brazil","Department of Mathematics, Baylor University, One Bear Place #97328, Waco, TX 76798-7328, USA","Department of Mathematics and Computer Science, Rhodes College, 2000 N. Parkway, Memphis, TN 38112"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada, Universidade Federal do Rio de Janeiro, Avenedo Athos da Silveira Ramos 149, Centro de Tecnologia \u2014 Bloco C, CEP 21941-909 Rio de Janeiro, Brazil","institution_ids":["https://openalex.org/I122140584"]},{"raw_affiliation_string":"Department of Mathematics, Baylor University, One Bear Place #97328, Waco, TX 76798-7328, USA","institution_ids":["https://openalex.org/I157394403"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science, Rhodes College, 2000 N. Parkway, Memphis, TN 38112","institution_ids":["https://openalex.org/I117979880"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085464884","display_name":"Daniel Herden","orcid":"https://orcid.org/0000-0002-4980-8778"},"institutions":[{"id":"https://openalex.org/I157394403","display_name":"Baylor University","ror":"https://ror.org/005781934","country_code":"US","type":"education","lineage":["https://openalex.org/I157394403"]},{"id":"https://openalex.org/I117979880","display_name":"Rhodes College","ror":"https://ror.org/049xfwy04","country_code":"US","type":"education","lineage":["https://openalex.org/I117979880"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel Herden","raw_affiliation_strings":["Department of Mathematics, Baylor University, One Bear Place #97328, Waco, TX 76798-7328, USA","Department of Mathematics and Computer Science, Rhodes College, 2000 N. Parkway, Memphis, TN 38112"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Baylor University, One Bear Place #97328, Waco, TX 76798-7328, USA","institution_ids":["https://openalex.org/I157394403"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science, Rhodes College, 2000 N. Parkway, Memphis, TN 38112","institution_ids":["https://openalex.org/I117979880"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044302531","display_name":"Christopher Seaton","orcid":"https://orcid.org/0000-0001-8545-2599"},"institutions":[{"id":"https://openalex.org/I117979880","display_name":"Rhodes College","ror":"https://ror.org/049xfwy04","country_code":"US","type":"education","lineage":["https://openalex.org/I117979880"]},{"id":"https://openalex.org/I157394403","display_name":"Baylor University","ror":"https://ror.org/005781934","country_code":"US","type":"education","lineage":["https://openalex.org/I157394403"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christopher Seaton","raw_affiliation_strings":["Department of Mathematics and Computer Science, Rhodes College, 2000 North Parkway, Memphis, TN 38112, USA","Department of Mathematics, Baylor University, One Bear Place #97328, Waco, TX 76798-7328, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Rhodes College, 2000 North Parkway, Memphis, TN 38112, USA","institution_ids":["https://openalex.org/I117979880"]},{"raw_affiliation_string":"Department of Mathematics, Baylor University, One Bear Place #97328, Waco, TX 76798-7328, USA","institution_ids":["https://openalex.org/I157394403"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5065397503"],"corresponding_institution_ids":["https://openalex.org/I117979880","https://openalex.org/I122140584","https://openalex.org/I157394403"],"apc_list":null,"apc_paid":null,"fwci":1.5408,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.82008608,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"30","issue":"07","first_page":"1323","last_page":"1357"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9998999834060669,"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":0.9998999834060669,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9998000264167786,"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/mathematics","display_name":"Mathematics","score":0.9091441631317139},{"id":"https://openalex.org/keywords/symplectic-geometry","display_name":"Symplectic geometry","score":0.7195004224777222},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.6966153383255005},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.6379667520523071},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5020575523376465},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.43004193902015686}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9091441631317139},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.7195004224777222},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.6966153383255005},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.6379667520523071},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5020575523376465},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.43004193902015686},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196720500435","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196720500435","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W80312135","https://openalex.org/W614287400","https://openalex.org/W644150847","https://openalex.org/W1492843823","https://openalex.org/W1497071382","https://openalex.org/W1507751798","https://openalex.org/W1526421297","https://openalex.org/W1584927588","https://openalex.org/W1598410915","https://openalex.org/W1664107667","https://openalex.org/W1908483350","https://openalex.org/W1955565830","https://openalex.org/W1967075232","https://openalex.org/W1972386730","https://openalex.org/W1976107596","https://openalex.org/W2005141684","https://openalex.org/W2022971738","https://openalex.org/W2029126093","https://openalex.org/W2040371959","https://openalex.org/W2051388657","https://openalex.org/W2078393607","https://openalex.org/W2080539870","https://openalex.org/W2089811736","https://openalex.org/W2102126064","https://openalex.org/W2113055611","https://openalex.org/W2116319358","https://openalex.org/W2140094741","https://openalex.org/W2335719489","https://openalex.org/W2495029002","https://openalex.org/W2584453131","https://openalex.org/W2624385320","https://openalex.org/W2735584556","https://openalex.org/W2963134911","https://openalex.org/W2964157164","https://openalex.org/W3098001113","https://openalex.org/W3098007167","https://openalex.org/W3104619845","https://openalex.org/W3105950105","https://openalex.org/W3106106736","https://openalex.org/W3125075313","https://openalex.org/W4240332533","https://openalex.org/W4256666875","https://openalex.org/W4256683994"],"related_works":["https://openalex.org/W2187058597","https://openalex.org/W1972361952","https://openalex.org/W4297967242","https://openalex.org/W4385970320","https://openalex.org/W2021613246","https://openalex.org/W2769537058","https://openalex.org/W4301808655","https://openalex.org/W2522170085","https://openalex.org/W2973399580","https://openalex.org/W2050868116"],"abstract_inverted_index":{"We":[0],"compute":[1,55,79],"the":[2,6,14,29,34,38,48,60,76,80,84],"Hilbert":[3,39,49,81],"series":[4,40,50,82],"of":[5,9,33,37,62,68,83,86,88],"graded":[7],"algebra":[8],"real":[10],"regular":[11],"functions":[12],"on":[13],"symplectic":[15],"quotient":[16],"associated":[17],"to":[18,54],"an":[19,25,52,89],"[Formula:":[20,42,72,91,95],"see":[21,43,73,92,96],"text]-module":[22,97],"and":[23,57],"give":[24,59],"explicit":[26],"expression":[27,46],"for":[28,47,65],"first":[30,102],"nonzero":[31],"coefficient":[32],"Laurent":[35,104],"expansion":[36],"at":[41,70],"text].":[44,74],"Our":[45],"indicates":[51],"algorithm":[53,64],"it,":[56],"we":[58,78],"output":[61],"this":[63],"all":[66],"representations":[67],"dimension":[69],"most":[71],"Along":[75],"way,":[77],"module":[85],"covariants":[87],"arbitrary":[90],"text]-":[93],"or":[94],"as":[98,100],"well":[99],"its":[101],"three":[103],"coefficients.":[105]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2020-07-29T00:00:00"}
