{"id":"https://openalex.org/W7223048152","doi":"https://doi.org/10.48550/arxiv.2610.25771","title":"Lusztig's asymptotic algebra and a cell factorisation for the second lowest two-sided cell in type $\\tilde{B}_n$","display_name":"Lusztig's asymptotic algebra and a cell factorisation for the second lowest two-sided cell in type $\\tilde{B}_n$","publication_year":2026,"publication_date":"2026-10-19","ids":{"openalex":"https://openalex.org/W7223048152","doi":"https://doi.org/10.48550/arxiv.2610.25771"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.25771","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.25771","pdf_url":"https://arxiv.org/pdf/2610.25771","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/2610.25771","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003991587","display_name":"James Parkinson","orcid":"https://orcid.org/0000-0002-1924-9127","observed_orcids":["https://orcid.org/0000-0002-1924-9127"]},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Parkinson, James","raw_affiliation_strings":["School of Mathematics and Statistics , University of Sydney , NSW 2006 , Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , University of Sydney , NSW 2006 , Australia","institution_ids":["https://openalex.org/I129604602"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5003991587"],"corresponding_institution_ids":["https://openalex.org/I129604602"],"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.5077999830245972,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.5077999830245972,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.32910001277923584,"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":0.13760000467300415,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/two-sided-cells","display_name":"two-sided cells","score":0.8999999761581421},{"id":"https://openalex.org/keywords/extended-affine-weyl-groups","display_name":"extended affine Weyl groups","score":0.8080000281333923},{"id":"https://openalex.org/keywords/matrix-algebra","display_name":"matrix algebra","score":0.453000009059906},{"id":"https://openalex.org/keywords/representation-ring","display_name":"representation ring","score":0.6639999747276306},{"id":"https://openalex.org/keywords/symplectic-group","display_name":"symplectic group","score":0.8309999704360962},{"id":"https://openalex.org/keywords/involutions","display_name":"involutions","score":0.9829999804496765}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7932000160217285},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.6705999970436096},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5634999871253967},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5541999936103821},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.508400022983551},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5002999901771545},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.4794999957084656},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.45590001344680786},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4404999911785126},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4352000057697296},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.43209999799728394},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4242999851703644},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4074999988079071},{"id":"https://openalex.org/C169171071","wikidata":"https://www.wikidata.org/wiki/Q5449241","display_name":"Filtered algebra","level":3,"score":0.40700000524520874},{"id":"https://openalex.org/C120047569","wikidata":"https://www.wikidata.org/wiki/Q92795049","display_name":"Group algebra","level":3,"score":0.3986999988555908},{"id":"https://openalex.org/C100899422","wikidata":"https://www.wikidata.org/wiki/Q5058347","display_name":"Cellular algebra","level":4,"score":0.3499000072479248},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.3474999964237213},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3337000012397766},{"id":"https://openalex.org/C185579658","wikidata":"https://www.wikidata.org/wiki/Q3554813","display_name":"Affine variety","level":3,"score":0.3336000144481659},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.33219999074935913},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.3231000006198883},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3188999891281128},{"id":"https://openalex.org/C138354692","wikidata":"https://www.wikidata.org/wiki/Q1231309","display_name":"Division algebra","level":4,"score":0.30799999833106995},{"id":"https://openalex.org/C191413488","wikidata":"https://www.wikidata.org/wiki/Q1892554","display_name":"Operator algebra","level":2,"score":0.2964000105857849},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.28859999775886536},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.2736000120639801},{"id":"https://openalex.org/C24209939","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic formula","level":2,"score":0.26600000262260437},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.25589999556541443},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.25290000438690186}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.25771","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.25771","pdf_url":"https://arxiv.org/pdf/2610.25771","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.2610.25771","doi":"https://doi.org/10.48550/arxiv.2610.25771","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.25771","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:2610.25771","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.25771","pdf_url":"https://arxiv.org/pdf/2610.25771","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/W7223048152.pdf","grobid_xml":"https://content.openalex.org/works/W7223048152.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2075876578","https://openalex.org/W1841400806","https://openalex.org/W4318071401","https://openalex.org/W1544487365","https://openalex.org/W4399598196","https://openalex.org/W1615042582","https://openalex.org/W4400205201","https://openalex.org/W3184992486","https://openalex.org/W2060436110","https://openalex.org/W7204802348"],"abstract_inverted_index":{"We":[0],"determine":[1],"Lusztig's":[2,71],"asymptotic":[3,63,81],"algebra":[4,30,82],"for":[5,20,84,148],"the":[6,12,32,40,54,62,77,80,105,136,144,151],"second":[7],"lowest":[8],"two-sided":[9],"cell~$\u0394_1$":[10],"in":[11,90,138],"equal":[13],"parameter":[14],"extended":[15],"affine":[16],"Weyl":[17],"group":[18,41],"$\\tilde{\\mathsf{B}}_n$":[19],"all":[21,118],"$n\\geq":[22],"2$,":[23],"realising":[24],"it":[25],"as":[26],"a":[27,66,94,133,141],"full":[28],"matrix":[29],"over":[31],"representation":[33],"ring":[34],"of":[35,42,50,56,61,79,96,104,107,120,129,135,143],"$\\mathsf{Sp}_{2n-2}(\\CC)\\times":[36],"C_2$":[37],"with":[38,125],"$C_2$":[39],"order~$2$.":[43],"Our":[44],"result":[45],"is":[46,93],"an":[47,101],"explicit":[48,102],"isomorphism":[49],"based":[51],"rings,":[52],"determining":[53],"image":[55],"each":[57],"basis":[58],"element":[59],"$\\mathsf{t}_w$":[60],"algebra.":[64],"As":[65],"consequence":[67],"we":[68],"verify":[69],"that":[70],"original":[72],"conjecture":[73],"from":[74],"1989":[75],"on":[76],"structure":[78],"holds":[83],"this":[85,108],"cell.":[86],"A":[87],"key":[88],"ingredient":[89],"our":[91],"proof":[92],"refinement":[95],"Shi's":[97],"description":[98],"of~$\u0394_1$,":[99],"giving":[100],"parametrisation":[103],"elements":[106],"cell":[109,114],"(a":[110],"\\textit{cell":[111],"factorisation}).":[112],"This":[113],"factorisation":[115],"simultaneously":[116],"describes":[117],"intersections":[119],"left":[121],"and":[122,127,140,150],"right":[123,152],"cells,":[124],"uniqueness":[126],"length-additivity":[128],"expressions.":[130],"Applications":[131],"include":[132],"classification":[134],"involutions":[137],"$\u0394_1$,":[139],"calculation":[142],"length":[145],"generating":[146],"functions":[147],"$\u0394_1$":[149],"cells":[153],"in~$\u0394_1$.":[154]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-21T00:00:00"}
