Quasifinite representations of classical Lie subalgebras of W∞,p

Autores
Garcia, José Ignacio; Liberati, Jose Ignacio
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We show that there are exactly two anti-involution σ± of the algebra of differential operators on the circle that are a multiple of p(t∂t) preserving the principal gradation (p ∈ C[x] non-constant). We classify the irreducible quasifinite highest weight representations of the central extension Db± p of the Lie subalgebra fixed by −σ±. The most important cases are the subalgebras Db± x of W∞, that are obtained when p(x) = x. In these cases we realize the irreducible quasifinite highest weight modules in terms of highest weight representation of the central extension of the Lie algebra of infinite matrices with finitely many non-zero diagonals over the algebra C[u]/(u m+1) and its classical Lie subalgebras of C and D types.
Fil: Garcia, José Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Fil: Liberati, Jose Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Materia
Algebra
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/230792
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Quasifinite representations of classical Lie subalgebras of W∞,pGarcia, José IgnacioLiberati, Jose IgnacioAlgebrahttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We show that there are exactly two anti-involution σ± of the algebra of differential operators on the circle that are a multiple of p(t∂t) preserving the principal gradation (p ∈ C[x] non-constant). We classify the irreducible quasifinite highest weight representations of the central extension Db± p of the Lie subalgebra fixed by −σ±. The most important cases are the subalgebras Db± x of W∞, that are obtained when p(x) = x. In these cases we realize the irreducible quasifinite highest weight modules in terms of highest weight representation of the central extension of the Lie algebra of infinite matrices with finitely many non-zero diagonals over the algebra C[u]/(u m+1) and its classical Lie subalgebras of C and D types.Fil: Garcia, José Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaFil: Liberati, Jose Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaAmerican Institute of Physics2012-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/230792Garcia, José Ignacio; Liberati, Jose Ignacio; Quasifinite representations of classical Lie subalgebras of W∞,p; American Institute of Physics; Journal of Mathematical Physics; 54; 7; 7-2012; 1-251111-1119CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1207.1151info:eu-repo/semantics/altIdentifier/doi/10.1063/1.4812556info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:22:21Zoai:ri.conicet.gov.ar:11336/230792instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-10 13:22:21.26CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Quasifinite representations of classical Lie subalgebras of W∞,p
title Quasifinite representations of classical Lie subalgebras of W∞,p
spellingShingle Quasifinite representations of classical Lie subalgebras of W∞,p
Garcia, José Ignacio
Algebra
title_short Quasifinite representations of classical Lie subalgebras of W∞,p
title_full Quasifinite representations of classical Lie subalgebras of W∞,p
title_fullStr Quasifinite representations of classical Lie subalgebras of W∞,p
title_full_unstemmed Quasifinite representations of classical Lie subalgebras of W∞,p
title_sort Quasifinite representations of classical Lie subalgebras of W∞,p
dc.creator.none.fl_str_mv Garcia, José Ignacio
Liberati, Jose Ignacio
author Garcia, José Ignacio
author_facet Garcia, José Ignacio
Liberati, Jose Ignacio
author_role author
author2 Liberati, Jose Ignacio
author2_role author
dc.subject.none.fl_str_mv Algebra
topic Algebra
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We show that there are exactly two anti-involution σ± of the algebra of differential operators on the circle that are a multiple of p(t∂t) preserving the principal gradation (p ∈ C[x] non-constant). We classify the irreducible quasifinite highest weight representations of the central extension Db± p of the Lie subalgebra fixed by −σ±. The most important cases are the subalgebras Db± x of W∞, that are obtained when p(x) = x. In these cases we realize the irreducible quasifinite highest weight modules in terms of highest weight representation of the central extension of the Lie algebra of infinite matrices with finitely many non-zero diagonals over the algebra C[u]/(u m+1) and its classical Lie subalgebras of C and D types.
Fil: Garcia, José Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Fil: Liberati, Jose Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
description We show that there are exactly two anti-involution σ± of the algebra of differential operators on the circle that are a multiple of p(t∂t) preserving the principal gradation (p ∈ C[x] non-constant). We classify the irreducible quasifinite highest weight representations of the central extension Db± p of the Lie subalgebra fixed by −σ±. The most important cases are the subalgebras Db± x of W∞, that are obtained when p(x) = x. In these cases we realize the irreducible quasifinite highest weight modules in terms of highest weight representation of the central extension of the Lie algebra of infinite matrices with finitely many non-zero diagonals over the algebra C[u]/(u m+1) and its classical Lie subalgebras of C and D types.
publishDate 2012
dc.date.none.fl_str_mv 2012-07
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/230792
Garcia, José Ignacio; Liberati, Jose Ignacio; Quasifinite representations of classical Lie subalgebras of W∞,p; American Institute of Physics; Journal of Mathematical Physics; 54; 7; 7-2012; 1-25
1111-1119
CONICET Digital
CONICET
url http://hdl.handle.net/11336/230792
identifier_str_mv Garcia, José Ignacio; Liberati, Jose Ignacio; Quasifinite representations of classical Lie subalgebras of W∞,p; American Institute of Physics; Journal of Mathematical Physics; 54; 7; 7-2012; 1-25
1111-1119
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1207.1151
info:eu-repo/semantics/altIdentifier/doi/10.1063/1.4812556
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Institute of Physics
publisher.none.fl_str_mv American Institute of Physics
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.493442

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