{"id":"https://openalex.org/W4385327770","doi":"https://doi.org/10.48550/arxiv.2307.13904","title":"Schubert calculus in Lie groups","display_name":"Schubert calculus in Lie groups","publication_year":2023,"publication_date":"2023-07-26","ids":{"openalex":"https://openalex.org/W4385327770","doi":"https://doi.org/10.48550/arxiv.2307.13904"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2307.13904","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2307.13904","pdf_url":"https://arxiv.org/pdf/2307.13904","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2307.13904","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101365146","display_name":"Haibao Duan","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Duan, Haibao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5101365146"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9452999830245972,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9452999830245972,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.03269999846816063,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.006899999920278788,"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/schubert-calculus","display_name":"Schubert calculus","score":1.0},{"id":"https://openalex.org/keywords/flag-varieties","display_name":"flag varieties","score":0.7089999914169312},{"id":"https://openalex.org/keywords/maximal-torus","display_name":"maximal torus","score":0.7599999904632568},{"id":"https://openalex.org/keywords/serre-spectral-sequence","display_name":"Serre spectral sequence","score":0.9269999861717224},{"id":"https://openalex.org/keywords/integral-cohomology-ring","display_name":"integral cohomology ring","score":0.9610000252723694}],"concepts":[{"id":"https://openalex.org/C169843257","wikidata":"https://www.wikidata.org/wiki/Q7432936","display_name":"Schubert calculus","level":3,"score":0.9197055101394653},{"id":"https://openalex.org/C197893656","wikidata":"https://www.wikidata.org/wiki/Q1000120","display_name":"Maximal torus","level":5,"score":0.7930213212966919},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7646922469139099},{"id":"https://openalex.org/C115491206","wikidata":"https://www.wikidata.org/wiki/Q938283","display_name":"Generalized flag variety","level":3,"score":0.7547024488449097},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.7163304090499878},{"id":"https://openalex.org/C54486226","wikidata":"https://www.wikidata.org/wiki/Q493941","display_name":"Fibration","level":3,"score":0.6964843273162842},{"id":"https://openalex.org/C2776730729","wikidata":"https://www.wikidata.org/wiki/Q1392130","display_name":"Flag (linear algebra)","level":3,"score":0.6845179796218872},{"id":"https://openalex.org/C178609977","wikidata":"https://www.wikidata.org/wiki/Q3503315","display_name":"Spectral sequence","level":3,"score":0.6767734289169312},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6048656105995178},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.5383760333061218},{"id":"https://openalex.org/C2779185822","wikidata":"https://www.wikidata.org/wiki/Q5141399","display_name":"Cohomology ring","level":4,"score":0.4632388949394226},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.4421572983264923},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.41115960478782654},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3989354968070984},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3350818157196045},{"id":"https://openalex.org/C72738302","wikidata":"https://www.wikidata.org/wiki/Q5384738","display_name":"Equivariant cohomology","level":3,"score":0.13042014837265015},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11136862635612488},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.08831050992012024},{"id":"https://openalex.org/C5106717","wikidata":"https://www.wikidata.org/wiki/Q3427416","display_name":"Fundamental representation","level":4,"score":0.0829218327999115},{"id":"https://openalex.org/C162929932","wikidata":"https://www.wikidata.org/wiki/Q129638","display_name":"Grassmannian","level":2,"score":0.07611656188964844},{"id":"https://openalex.org/C183877218","wikidata":"https://www.wikidata.org/wiki/Q7979858","display_name":"Weight","level":3,"score":0.06049361824989319}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2307.13904","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2307.13904","pdf_url":"https://arxiv.org/pdf/2307.13904","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.2307.13904","doi":"https://doi.org/10.48550/arxiv.2307.13904","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2307.13904","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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2307.13904","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2307.13904","pdf_url":"https://arxiv.org/pdf/2307.13904","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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4385327770.pdf","grobid_xml":"https://content.openalex.org/works/W4385327770.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2200265135","https://openalex.org/W198140332","https://openalex.org/W2273391126","https://openalex.org/W1591661675","https://openalex.org/W2996134596","https://openalex.org/W2946208708","https://openalex.org/W1487824735","https://openalex.org/W2903678920","https://openalex.org/W1789251938","https://openalex.org/W182584903"],"abstract_inverted_index":{"Let":[0],"$G$":[1],"be":[2],"a":[3,7],"Lie":[4,43],"group":[5],"with":[6,19],"maximal":[8],"torus":[9],"$T$.":[10],"Combining":[11],"Schubert":[12],"calculus":[13],"in":[14],"the":[15,20,25,31],"flag":[16],"manifold":[17],"$G/T$":[18],"Serre":[21],"spectral":[22],"sequence":[23],"of":[24],"fibration":[26],"$G\\rightarrow":[27],"G/T$,":[28],"we":[29],"construct":[30],"integral":[32],"cohomology":[33],"ring":[34],"$H^{\\ast}(G)$":[35],"uniformly":[36],"for":[37],"all":[38],"compact":[39],"and":[40],"simply":[41],"connected":[42],"groups":[44],"$G$.":[45]},"counts_by_year":[{"year":2024,"cited_by_count":2}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}
