Schubert Derivations on the Infinite Wedge Power
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1007/s00574-020-00195-9 http://hdl.handle.net/11449/201520 |
Resumo: | The Schubert derivation is a distinguished Hasse–Schmidt derivation on the exterior algebra of a free abelian group, encoding the formalism of Schubert calculus for all Grassmannians at once. The purpose of this paper is to extend the Schubert derivation to the infinite exterior power of a free Z-module of infinite rank (fermionic Fock space). Classical vertex operators naturally arise from the integration by parts formula, that also recovers the generating function occurring in the bosonic vertex representation of the Lie algebra gl∞(Z) , due to Date, Jimbo, Kashiwara and Miwa (DJKM). In the present framework, the DJKM result will be interpreted as a limit case of the following general observation: the singular cohomology of the complex Grassmannian G(r, n) is an irreducible representation of the Lie algebra of n× n square matrices. |
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Repositório Institucional da UNESP |
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Schubert Derivations on the Infinite Wedge PowerBosonic and Fermionic Fock spacesBosonic vertex representation of Date–Jimbo–Kashiwara–MiwaHasse–Schmidt derivations on exterior algebrasSchubert derivations on infinite wedge powersVertex operatorsThe Schubert derivation is a distinguished Hasse–Schmidt derivation on the exterior algebra of a free abelian group, encoding the formalism of Schubert calculus for all Grassmannians at once. The purpose of this paper is to extend the Schubert derivation to the infinite exterior power of a free Z-module of infinite rank (fermionic Fock space). Classical vertex operators naturally arise from the integration by parts formula, that also recovers the generating function occurring in the bosonic vertex representation of the Lie algebra gl∞(Z) , due to Date, Jimbo, Kashiwara and Miwa (DJKM). In the present framework, the DJKM result will be interpreted as a limit case of the following general observation: the singular cohomology of the complex Grassmannian G(r, n) is an irreducible representation of the Lie algebra of n× n square matrices.Dipartimento di Scienze Matematiche Politecnico di TorinoIbilce UNESP, Campus de São José do Rio PretoIbilce UNESP, Campus de São José do Rio PretoPolitecnico di TorinoUniversidade Estadual Paulista (Unesp)Gatto, LetterioSalehyan, Parham [UNESP]2020-12-12T02:34:43Z2020-12-12T02:34:43Z2020-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1007/s00574-020-00195-9Bulletin of the Brazilian Mathematical Society.1678-7544http://hdl.handle.net/11449/20152010.1007/s00574-020-00195-92-s2.0-8507892491533558402196800310000-0001-5885-5034Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengBulletin of the Brazilian Mathematical Societyinfo:eu-repo/semantics/openAccess2021-10-22T20:11:18Zoai:repositorio.unesp.br:11449/201520Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462021-10-22T20:11:18Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Schubert Derivations on the Infinite Wedge Power |
title |
Schubert Derivations on the Infinite Wedge Power |
spellingShingle |
Schubert Derivations on the Infinite Wedge Power Gatto, Letterio Bosonic and Fermionic Fock spaces Bosonic vertex representation of Date–Jimbo–Kashiwara–Miwa Hasse–Schmidt derivations on exterior algebras Schubert derivations on infinite wedge powers Vertex operators |
title_short |
Schubert Derivations on the Infinite Wedge Power |
title_full |
Schubert Derivations on the Infinite Wedge Power |
title_fullStr |
Schubert Derivations on the Infinite Wedge Power |
title_full_unstemmed |
Schubert Derivations on the Infinite Wedge Power |
title_sort |
Schubert Derivations on the Infinite Wedge Power |
author |
Gatto, Letterio |
author_facet |
Gatto, Letterio Salehyan, Parham [UNESP] |
author_role |
author |
author2 |
Salehyan, Parham [UNESP] |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Politecnico di Torino Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Gatto, Letterio Salehyan, Parham [UNESP] |
dc.subject.por.fl_str_mv |
Bosonic and Fermionic Fock spaces Bosonic vertex representation of Date–Jimbo–Kashiwara–Miwa Hasse–Schmidt derivations on exterior algebras Schubert derivations on infinite wedge powers Vertex operators |
topic |
Bosonic and Fermionic Fock spaces Bosonic vertex representation of Date–Jimbo–Kashiwara–Miwa Hasse–Schmidt derivations on exterior algebras Schubert derivations on infinite wedge powers Vertex operators |
description |
The Schubert derivation is a distinguished Hasse–Schmidt derivation on the exterior algebra of a free abelian group, encoding the formalism of Schubert calculus for all Grassmannians at once. The purpose of this paper is to extend the Schubert derivation to the infinite exterior power of a free Z-module of infinite rank (fermionic Fock space). Classical vertex operators naturally arise from the integration by parts formula, that also recovers the generating function occurring in the bosonic vertex representation of the Lie algebra gl∞(Z) , due to Date, Jimbo, Kashiwara and Miwa (DJKM). In the present framework, the DJKM result will be interpreted as a limit case of the following general observation: the singular cohomology of the complex Grassmannian G(r, n) is an irreducible representation of the Lie algebra of n× n square matrices. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-12-12T02:34:43Z 2020-12-12T02:34:43Z 2020-01-01 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1007/s00574-020-00195-9 Bulletin of the Brazilian Mathematical Society. 1678-7544 http://hdl.handle.net/11449/201520 10.1007/s00574-020-00195-9 2-s2.0-85078924915 3355840219680031 0000-0001-5885-5034 |
url |
http://dx.doi.org/10.1007/s00574-020-00195-9 http://hdl.handle.net/11449/201520 |
identifier_str_mv |
Bulletin of the Brazilian Mathematical Society. 1678-7544 10.1007/s00574-020-00195-9 2-s2.0-85078924915 3355840219680031 0000-0001-5885-5034 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Bulletin of the Brazilian Mathematical Society |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1799964891298136064 |