{"id":"https://openalex.org/W7214284450","doi":"https://doi.org/10.48550/arxiv.2609.30242","title":"A Peterson program for general Schubert varieties and mirror symmetry","display_name":"A Peterson program for general Schubert varieties and mirror symmetry","publication_year":2026,"publication_date":"2026-09-24","ids":{"openalex":"https://openalex.org/W7214284450","doi":"https://doi.org/10.48550/arxiv.2609.30242"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.30242","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30242","pdf_url":"https://arxiv.org/pdf/2609.30242","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/2609.30242","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5138268985","display_name":"Changzheng Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li, Changzheng","raw_affiliation_strings":["School of Mathematics , Sun Yat-sen University , Guangzhou 510275 , P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , Sun Yat-sen University , Guangzhou 510275 , P.R. China","institution_ids":["https://openalex.org/I157773358"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029482516","display_name":"Konstanze Rietsch","orcid":"https://orcid.org/0000-0002-3592-2940","observed_orcids":["https://orcid.org/0000-0002-3592-2940"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rietsch, Konstanze","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5152949431","display_name":"Mingzhi Yang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yang, Mingzhi","raw_affiliation_strings":["School of Mathematics , Sun Yat-sen University , Guangzhou 510275 , P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , Sun Yat-sen University , Guangzhou 510275 , P.R. China","institution_ids":["https://openalex.org/I157773358"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.7666000127792358,"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":0.7666000127792358,"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":0.09589999914169312,"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":0.04340000078082085,"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/schubert-varieties","display_name":"Schubert varieties","score":0.9020000100135803},{"id":"https://openalex.org/keywords/quantum-cohomology","display_name":"quantum cohomology","score":0.9729999899864197},{"id":"https://openalex.org/keywords/mirror-symmetry","display_name":"mirror symmetry","score":0.9629999995231628},{"id":"https://openalex.org/keywords/superpotential","display_name":"superpotential","score":0.8140000104904175},{"id":"https://openalex.org/keywords/partial-flag-varieties","display_name":"partial flag varieties","score":0.7870000004768372}],"concepts":[{"id":"https://openalex.org/C47158899","wikidata":"https://www.wikidata.org/wiki/Q7432938","display_name":"Schubert variety","level":2,"score":0.8044999837875366},{"id":"https://openalex.org/C97912942","wikidata":"https://www.wikidata.org/wiki/Q7432937","display_name":"Schubert polynomial","level":2,"score":0.7986999750137329},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7542999982833862},{"id":"https://openalex.org/C169843257","wikidata":"https://www.wikidata.org/wiki/Q7432936","display_name":"Schubert calculus","level":3,"score":0.7202000021934509},{"id":"https://openalex.org/C2776730729","wikidata":"https://www.wikidata.org/wiki/Q1392130","display_name":"Flag (linear algebra)","level":3,"score":0.6237999796867371},{"id":"https://openalex.org/C136660716","wikidata":"https://www.wikidata.org/wiki/Q7269022","display_name":"Quantum cohomology","level":4,"score":0.6072999835014343},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5927000045776367},{"id":"https://openalex.org/C162929932","wikidata":"https://www.wikidata.org/wiki/Q129638","display_name":"Grassmannian","level":2,"score":0.5807999968528748},{"id":"https://openalex.org/C185579658","wikidata":"https://www.wikidata.org/wiki/Q3554813","display_name":"Affine variety","level":3,"score":0.5638999938964844},{"id":"https://openalex.org/C188374626","wikidata":"https://www.wikidata.org/wiki/Q5914418","display_name":"Mirror symmetry","level":2,"score":0.5126000046730042},{"id":"https://openalex.org/C2779185822","wikidata":"https://www.wikidata.org/wiki/Q5141399","display_name":"Cohomology ring","level":4,"score":0.4893999993801117},{"id":"https://openalex.org/C5052557","wikidata":"https://www.wikidata.org/wiki/Q1528306","display_name":"Toric variety","level":2,"score":0.4713999927043915},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.43799999356269836},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.4259999990463257},{"id":"https://openalex.org/C54486226","wikidata":"https://www.wikidata.org/wiki/Q493941","display_name":"Fibration","level":3,"score":0.42590001225471497},{"id":"https://openalex.org/C62139920","wikidata":"https://www.wikidata.org/wiki/Q3554818","display_name":"Projective variety","level":2,"score":0.4203000068664551},{"id":"https://openalex.org/C115491206","wikidata":"https://www.wikidata.org/wiki/Q938283","display_name":"Generalized flag variety","level":3,"score":0.41429999470710754},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.3885999917984009},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.38839998841285706},{"id":"https://openalex.org/C72738302","wikidata":"https://www.wikidata.org/wiki/Q5384738","display_name":"Equivariant cohomology","level":3,"score":0.3700000047683716},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33410000801086426},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.3246000111103058},{"id":"https://openalex.org/C39757861","wikidata":"https://www.wikidata.org/wiki/Q1395814","display_name":"Fano plane","level":2,"score":0.32260000705718994},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.3154999911785126},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3109999895095825},{"id":"https://openalex.org/C84254916","wikidata":"https://www.wikidata.org/wiki/Q2981889","display_name":"Motivic cohomology","level":5,"score":0.2856000065803528},{"id":"https://openalex.org/C114825156","wikidata":"https://www.wikidata.org/wiki/Q4775328","display_name":"Antisymmetry","level":2,"score":0.28450000286102295},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.28119999170303345},{"id":"https://openalex.org/C121451207","wikidata":"https://www.wikidata.org/wiki/Q3978062","display_name":"Supermanifold","level":2,"score":0.27059999108314514},{"id":"https://openalex.org/C2780580338","wikidata":"https://www.wikidata.org/wiki/Q577835","display_name":"Adjunction","level":2,"score":0.2669000029563904},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C7979169","wikidata":"https://www.wikidata.org/wiki/Q1142143","display_name":"Cotangent bundle","level":3,"score":0.26179999113082886},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.25870001316070557},{"id":"https://openalex.org/C165761256","wikidata":"https://www.wikidata.org/wiki/Q648995","display_name":"Algebraic variety","level":3,"score":0.2567000091075897},{"id":"https://openalex.org/C2779165322","wikidata":"https://www.wikidata.org/wiki/Q546145","display_name":"Compactification (mathematics)","level":2,"score":0.2556000053882599}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.30242","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30242","pdf_url":"https://arxiv.org/pdf/2609.30242","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.2609.30242","doi":"https://doi.org/10.48550/arxiv.2609.30242","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.30242","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:2609.30242","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30242","pdf_url":"https://arxiv.org/pdf/2609.30242","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/W7214284450.pdf","grobid_xml":"https://content.openalex.org/works/W7214284450.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4407618162","https://openalex.org/W4387097657","https://openalex.org/W4391376198","https://openalex.org/W4307934230","https://openalex.org/W7099714060","https://openalex.org/W1533218804","https://openalex.org/W2171365210","https://openalex.org/W4392303272","https://openalex.org/W4387390158","https://openalex.org/W7099970152"],"abstract_inverted_index":{"We":[0,112],"initiate":[1],"a":[2,26,35,51,62,79,176,248],"`Peterson":[3],"program'":[4],"that":[5,24,66,101,117,179,232,237],"seeks":[6],"to":[7,19,43,83,161],"extend":[8],"Dale":[9],"Peterson's":[10],"theory":[11],"for":[12,89,118,217,239],"the":[13,38,69,90,108,114,123,127,132,141,162,168,183,194,202,206,223,252],"quantum":[14,133,142,185],"cohomology":[15,134,186],"of":[16,37,126,136,167,172,188,197,205,210,251],"flag":[17,53,73,91,227],"varieties":[18,92,122,148,242],"arbitrary":[20,45],"Schubert":[21,46,121,147,220,241],"varieties,":[22],"and":[23,98,174,229,245],"incorporates":[25],"mirror-symmetric":[27],"approach.":[28],"In":[29],"this":[30],"first":[31],"paper":[32],"we":[33,77,99,154,180,230],"introduce":[34],"generalisation":[36,59],"(localised)":[39],"Peterson":[40,110,129,159],"variety":[41,47,54,74,130,160],"associated":[42,82],"an":[44],"$\\check":[48,55,84,93,137,151,189,211],"X_{w,P}$":[49,138],"inside":[50],"partial":[52,177],"G/\\check":[56,94,152,199],"P$.":[57],"This":[58],"is":[60],"possibly":[61],"non-reduced":[63],"affine":[64],"scheme":[65],"lies":[67],"in":[68,150,191,222],"Langlands":[70],"dual":[71],"full":[72,184],"$G/B$.":[75],"Additionally,":[76],"construct":[78,175],"Lie-theoretic":[80],"`superpotential'":[81],"X_{w,P}$,":[85],"generalising":[86],"earlier":[87],"ones":[88],"P$":[95],"from":[96],"[Rie08],":[97],"show":[100,231],"its":[102],"relative":[103],"critical":[104],"point":[105],"locus":[106],"recovers":[107,131],"generalised":[109,128,158],"variety.":[111],"make":[113],"key":[115],"conjecture":[116,181],"smooth":[119,145,219],"Fano":[120,146],"coordinate":[124],"ring":[125,135,187],"localised":[139],"at":[140],"parameters.":[143],"For":[144],"$X_{w,B}$":[149],"B$":[153],"furthermore":[155],"map":[156],"our":[157,233],"cotangent":[163],"bundle":[164],"$\\mathcal":[165],"T^*(T)$":[166],"maximal":[169],"torus":[170],"$T$":[171],"$G$":[173],"compactification":[178],"models":[182],"X_{w,B}$,":[190],"analogy":[192],"with":[193,236],"Givental-Kim":[195],"presentation":[196],"$QH^*(\\check":[198],"B)$":[200],"via":[201],"degenerate":[203],"leaf":[204],"Kostant":[207],"Toda":[208],"lattice":[209],"G$.":[212],"These":[213],"conjectures":[214],"are":[215],"verified":[216],"all":[218],"divisors":[221],"complete":[224],"type":[225],"$A$":[226],"variety,":[228],"superpotential":[234],"agrees":[235],"introduced":[238],"Grassmannian":[240],"by":[243],"Rietsch":[244],"Williams,":[246],"after":[247],"suitable":[249],"isomorphism":[250],"domains.":[253]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-26T00:00:00"}
