The cohomology of the Grassmannian is a gln-module
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1080/00927872.2019.1640240 http://hdl.handle.net/11449/190589 |
Resumo: | The integral singular cohomology ring of the Grassmann variety parametrizing r-dimensional subspaces in the n-dimensional complex vector space is naturally an irreducible representation of the Lie algebra (Formula presented.) of all the n × n matrices with integral entries. The simplest case, r = 1, recovers the well known fact that any vector space is a module over the Lie algebra of its own endomorphisms. The other extremal case, (Formula presented.) corresponds to the bosonic vertex representation of the Lie algebra (Formula presented.) on the polynomial ring in infinitely many indeterminates, due to Date, Jimbo, Kashiwara and Miwa. In the present article we provide the structure of this irreducible representation explicitly, by means of a distinguished Hasse-Schmidt derivation on an exterior algebra, borrowed from Schubert Calculus. |
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The cohomology of the Grassmannian is a gln-moduleBosonic vertex representation of Date-Jimbo-Kashiwara-Miwacohomology of the GrassmannianHasse-Schmidt derivations on exterior algebrasSchubert derivationsvertex operatorsThe integral singular cohomology ring of the Grassmann variety parametrizing r-dimensional subspaces in the n-dimensional complex vector space is naturally an irreducible representation of the Lie algebra (Formula presented.) of all the n × n matrices with integral entries. The simplest case, r = 1, recovers the well known fact that any vector space is a module over the Lie algebra of its own endomorphisms. The other extremal case, (Formula presented.) corresponds to the bosonic vertex representation of the Lie algebra (Formula presented.) on the polynomial ring in infinitely many indeterminates, due to Date, Jimbo, Kashiwara and Miwa. In the present article we provide the structure of this irreducible representation explicitly, by means of a distinguished Hasse-Schmidt derivation on an exterior algebra, borrowed from Schubert Calculus.Dipartimento di Scienze Matematiche Politecnico di TorinoInstitute of Biosciences Humanities and Exact Sciences São Paulo State University (UNESP)Institute of Biosciences Humanities and Exact Sciences São Paulo State University (UNESP)Politecnico di TorinoUniversidade Estadual Paulista (Unesp)Gatto, LetterioSalehyan, Parham [UNESP]2019-10-06T17:18:18Z2019-10-06T17:18:18Z2019-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1080/00927872.2019.1640240Communications in Algebra.1532-41250092-7872http://hdl.handle.net/11449/19058910.1080/00927872.2019.16402402-s2.0-8507096182233558402196800310000-0001-5885-5034Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengCommunications in Algebrainfo:eu-repo/semantics/openAccess2021-10-22T21:09:39Zoai:repositorio.unesp.br:11449/190589Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462021-10-22T21:09:39Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
The cohomology of the Grassmannian is a gln-module |
title |
The cohomology of the Grassmannian is a gln-module |
spellingShingle |
The cohomology of the Grassmannian is a gln-module Gatto, Letterio Bosonic vertex representation of Date-Jimbo-Kashiwara-Miwa cohomology of the Grassmannian Hasse-Schmidt derivations on exterior algebras Schubert derivations vertex operators |
title_short |
The cohomology of the Grassmannian is a gln-module |
title_full |
The cohomology of the Grassmannian is a gln-module |
title_fullStr |
The cohomology of the Grassmannian is a gln-module |
title_full_unstemmed |
The cohomology of the Grassmannian is a gln-module |
title_sort |
The cohomology of the Grassmannian is a gln-module |
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 vertex representation of Date-Jimbo-Kashiwara-Miwa cohomology of the Grassmannian Hasse-Schmidt derivations on exterior algebras Schubert derivations vertex operators |
topic |
Bosonic vertex representation of Date-Jimbo-Kashiwara-Miwa cohomology of the Grassmannian Hasse-Schmidt derivations on exterior algebras Schubert derivations vertex operators |
description |
The integral singular cohomology ring of the Grassmann variety parametrizing r-dimensional subspaces in the n-dimensional complex vector space is naturally an irreducible representation of the Lie algebra (Formula presented.) of all the n × n matrices with integral entries. The simplest case, r = 1, recovers the well known fact that any vector space is a module over the Lie algebra of its own endomorphisms. The other extremal case, (Formula presented.) corresponds to the bosonic vertex representation of the Lie algebra (Formula presented.) on the polynomial ring in infinitely many indeterminates, due to Date, Jimbo, Kashiwara and Miwa. In the present article we provide the structure of this irreducible representation explicitly, by means of a distinguished Hasse-Schmidt derivation on an exterior algebra, borrowed from Schubert Calculus. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-10-06T17:18:18Z 2019-10-06T17:18:18Z 2019-01-01 |
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/10.1080/00927872.2019.1640240 Communications in Algebra. 1532-4125 0092-7872 http://hdl.handle.net/11449/190589 10.1080/00927872.2019.1640240 2-s2.0-85070961822 3355840219680031 0000-0001-5885-5034 |
url |
http://dx.doi.org/10.1080/00927872.2019.1640240 http://hdl.handle.net/11449/190589 |
identifier_str_mv |
Communications in Algebra. 1532-4125 0092-7872 10.1080/00927872.2019.1640240 2-s2.0-85070961822 3355840219680031 0000-0001-5885-5034 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Communications in Algebra |
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_ |
1799965476616404992 |