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dc.contributor.author
Lauret, Emilio Agustin
dc.contributor.author
Miatello, Roberto Jorge
dc.date.available
2020-06-30T23:16:40Z
dc.date.issued
2020-03-02
dc.identifier.citation
Lauret, Emilio Agustin; Miatello, Roberto Jorge; Strong multiplicity one theorems for locally homogeneous spaces of compact type; American Mathematical Society; Proceedings of the American Mathematical Society; 148; 7; 02-3-2020; 3163-3173
dc.identifier.issn
0002-9939
dc.identifier.uri
http://hdl.handle.net/11336/108559
dc.description.abstract
Let G be a compact connected semisimple Lie group, let K be a closed subgroup of G, let Γ be a finite subgroup of G, and let τ be a finitedimensional representation of K. For π in the unitary dual G of G, denote by nΓ(π) its multiplicity in L2(Γ\G). We prove a strong multiplicity one theorem in the spirit of Bhagwat and Rajan, for the nΓ(π) for π in the set Gτ of irreducible τ-spherical representations of G. More precisely, for Γ and Γ finite subgroups of G, we prove that if nΓ(π) = nΓ (π) for all but finitely many π ∈ Gτ , then Γ and Γ are τ-representation equivalent, that is, nΓ(π) = nΓ (π) for all π ∈ Gτ . Moreover, when Gτ can be written as a finite union of strings of representations, we prove a finite version of the above result. For any finite subset Fτ of Gτ verifying some mild conditions, the values of the nΓ(π) for π ∈ Fτ determine the nΓ(π)’s for all π ∈ Gτ . In particular, for two finite subgroups Γ and Γ of G, if nΓ(π) = nΓ (π) for all π ∈ Fτ , then the equality holds for every π ∈ Gτ . We use algebraic methods involving generating functions and some facts from the representation theory of G.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
American Mathematical Society
dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
STRONG MULTIPLICITY ONE THEOREM
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RIGHT REGULAR REPRESENTATION
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REPRESENTATION EQUIVALENT
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Matemática Pura
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Matemáticas
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CIENCIAS NATURALES Y EXACTAS
dc.title
Strong multiplicity one theorems for locally homogeneous spaces of compact type
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2020-06-22T14:08:35Z
dc.identifier.eissn
1088-6826
dc.journal.volume
148
dc.journal.number
7
dc.journal.pagination
3163-3173
dc.journal.pais
Estados Unidos
dc.description.fil
Fil: Lauret, Emilio Agustin. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
dc.description.fil
Fil: Miatello, Roberto Jorge. 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
dc.journal.title
Proceedings of the American Mathematical Society
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/proc/2020-148-07/S0002-9939-2020-14980-5/home.html
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1804.08288
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1090/proc/14980
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