The conservation relation for cuspidal representations

Let π ∈ Cusp (U(Vn)) be a smooth cuspidal irreducible representation of a unitary group U(Vn) of dimension n over a non-Archimedean locally compact field. Let W± m the two isomorphism classes of Hermitian spaces of dimension m, and the denote by τ + ∈ Cusp U(W+m+) and τ− ∈ Cusp U(W−m−) the first non...

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Detalles Bibliográficos
Autor: Mínguez Espallargas, Alberto
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2012
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/47611
Acceso en línea:http://hdl.handle.net/11441/47611
https://doi.org/10.1007/s00208-011-0636-5
Access Level:acceso abierto
Palabra clave:Theta correspondence
Theta dichotomy
Representations of p-adic groups
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spelling The conservation relation for cuspidal representationsMínguez Espallargas, AlbertoTheta correspondenceTheta dichotomyRepresentations of p-adic groupsLet π ∈ Cusp (U(Vn)) be a smooth cuspidal irreducible representation of a unitary group U(Vn) of dimension n over a non-Archimedean locally compact field. Let W± m the two isomorphism classes of Hermitian spaces of dimension m, and the denote by τ + ∈ Cusp U(W+m+) and τ− ∈ Cusp U(W−m−) the first non-zero theta lifts of π. In this article we prove that m+ + m− = 2n + 2, which was conjectured in [M. Harris, S. S. Kudla, J. Sweet, Theta dichotomy for unitary groups, Journal of the AMS, vol. 9, pp. 941-1004 (1996), Speculations 7.5 and 7.6]. We prove similar equalities for the other dual pairs of type I : the symplecticorthogonal dual pairs and the quaternionic dual pairs.Engineering and Physical Sciences Research CouncilMinisterio de Educación y CienciaFondo Europeo de Desarrollo RegionalSpringerÁlgebraFQM218: Geometria Algebraica, Sistemas Diferenciales y Singularidades2012info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/47611https://doi.org/10.1007/s00208-011-0636-5reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésMathematische Annalen, 352, 179-188.EP/G001480/1MTM2007-66929http://download.springer.com/static/pdf/815/art%253A10.1007%252Fs00208-011-0636-5.pdf?originUrl=http%3A%2F%2Flink.springer.com%2Farticle%2F10.1007%2Fs00208-011-0636-5&token2=exp=1476699055~acl=%2Fstatic%2Fpdf%2F815%2Fart%25253A10.1007%25252Fs00208-011-0636-5.pdf%3ForiginUrl%3Dhttp%253A%252F%252Flink.springer.com%252Farticle%252F10.1007%252Fs00208-011-0636-5*~hmac=6ebcf1e2065a58cce51783f8568e93e8f521355eb5a589b8f3117058045af791info:eu-repo/semantics/openAccessoai:idus.us.es:11441/476112026-06-17T12:51:07Z
dc.title.none.fl_str_mv The conservation relation for cuspidal representations
title The conservation relation for cuspidal representations
spellingShingle The conservation relation for cuspidal representations
Mínguez Espallargas, Alberto
Theta correspondence
Theta dichotomy
Representations of p-adic groups
title_short The conservation relation for cuspidal representations
title_full The conservation relation for cuspidal representations
title_fullStr The conservation relation for cuspidal representations
title_full_unstemmed The conservation relation for cuspidal representations
title_sort The conservation relation for cuspidal representations
dc.creator.none.fl_str_mv Mínguez Espallargas, Alberto
author Mínguez Espallargas, Alberto
author_facet Mínguez Espallargas, Alberto
author_role author
dc.contributor.none.fl_str_mv Álgebra
FQM218: Geometria Algebraica, Sistemas Diferenciales y Singularidades
dc.subject.none.fl_str_mv Theta correspondence
Theta dichotomy
Representations of p-adic groups
topic Theta correspondence
Theta dichotomy
Representations of p-adic groups
description Let π ∈ Cusp (U(Vn)) be a smooth cuspidal irreducible representation of a unitary group U(Vn) of dimension n over a non-Archimedean locally compact field. Let W± m the two isomorphism classes of Hermitian spaces of dimension m, and the denote by τ + ∈ Cusp U(W+m+) and τ− ∈ Cusp U(W−m−) the first non-zero theta lifts of π. In this article we prove that m+ + m− = 2n + 2, which was conjectured in [M. Harris, S. S. Kudla, J. Sweet, Theta dichotomy for unitary groups, Journal of the AMS, vol. 9, pp. 941-1004 (1996), Speculations 7.5 and 7.6]. We prove similar equalities for the other dual pairs of type I : the symplecticorthogonal dual pairs and the quaternionic dual pairs.
publishDate 2012
dc.date.none.fl_str_mv 2012
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/47611
https://doi.org/10.1007/s00208-011-0636-5
url http://hdl.handle.net/11441/47611
https://doi.org/10.1007/s00208-011-0636-5
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Mathematische Annalen, 352, 179-188.
EP/G001480/1
MTM2007-66929
http://download.springer.com/static/pdf/815/art%253A10.1007%252Fs00208-011-0636-5.pdf?originUrl=http%3A%2F%2Flink.springer.com%2Farticle%2F10.1007%2Fs00208-011-0636-5&token2=exp=1476699055~acl=%2Fstatic%2Fpdf%2F815%2Fart%25253A10.1007%25252Fs00208-011-0636-5.pdf%3ForiginUrl%3Dhttp%253A%252F%252Flink.springer.com%252Farticle%252F10.1007%252Fs00208-011-0636-5*~hmac=6ebcf1e2065a58cce51783f8568e93e8f521355eb5a589b8f3117058045af791
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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