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dc.contributor.author
Miatello, Roberto Jorge  
dc.contributor.author
Lauret, Emilio Agustin  
dc.date.available
2022-10-12T17:57:24Z  
dc.date.issued
2021-11-10  
dc.identifier.citation
Miatello, Roberto Jorge; Lauret, Emilio Agustin; Strong representation equivalence for compact symmetric spaces of real rank one; Pacific Journal Mathematics; Pacific Journal Of Mathematics; 314; 2; 10-11-2021; 333-373  
dc.identifier.issn
0030-8730  
dc.identifier.uri
http://hdl.handle.net/11336/172762  
dc.description.abstract
Let G∕K be a simply connected compact irreducible symmetric space of real rank one. For each K-type τ we compare the notions of τ-representation equivalence with τ-isospectrality. We exhibit infinitely many K-types τ so that, for arbitrary discrete subgroups Γ and Γ´ of G, if the multiplicities of λ in the spectra of the Laplace operators acting on sections of the induced τ-vector bundles over Γ∖G∕K and Γ´∖G/K agree for all but finitely many λ, then Γ and Γ´ are τ-representation equivalent in G (i.e., dimHomG(Vπ,L2(Γ∖G))=dimHomG(Vπ,L2(Γ´∖G)) for all π∈?G satisfying HomK(Vτ,Vπ)≠0). In particular, Γ∖G∕K and Γ´∖G/K are τ-isospectral (i.e., the multiplicities agree for all λ).We specially study the case of p-form representations, i.e., the irreducible subrepresentations τ of the representation τp of K on the p-exterior power of the complexified cotangent bundle ∧pT∗CM. We show that for such τ, in most cases τ-isospectrality implies τ-representation equivalence. We construct an explicit counterexample for G/K=SO(4n)/SO(4n−1)≃S4n−1.  
dc.format
application/pdf  
dc.language.iso
eng  
dc.publisher
Pacific Journal Mathematics  
dc.rights
info:eu-repo/semantics/openAccess  
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/  
dc.subject
ISOSPECTRAL  
dc.subject
REPRESENTATION EQUIVALENT  
dc.subject
Τ-SPECTRUM  
dc.subject.classification
Matemática Pura  
dc.subject.classification
Matemáticas  
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS  
dc.title
Strong representation equivalence for compact symmetric spaces of real rank one  
dc.type
info:eu-repo/semantics/article  
dc.type
info:ar-repo/semantics/artículo  
dc.type
info:eu-repo/semantics/publishedVersion  
dc.date.updated
2022-09-19T16:06:54Z  
dc.identifier.eissn
1945-5844  
dc.journal.volume
314  
dc.journal.number
2  
dc.journal.pagination
333-373  
dc.journal.pais
Estados Unidos  
dc.journal.ciudad
California  
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.description.fil
Fil: Lauret, Emilio Agustin. Universidad Nacional del Sur. Departamento de Matemática; Argentina. 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.journal.title
Pacific Journal Of Mathematics  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://msp.org/pjm/2021/314-2/pjm-v314-n2-p05-p.pdf  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1812.09606  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.48550/arXiv.1812.09606