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dc.contributor.author
Fernández Culma, Edison Alberto
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dc.date.available
2016-12-07T16:55:12Z
dc.date.issued
2013-12
dc.identifier.citation
Fernández Culma, Edison Alberto; On distinguished orbits of reductive representations; Elsevier; Journal Of Algebra; 396; 12-2013; 61-81
dc.identifier.issn
0021-8693
dc.identifier.uri
http://hdl.handle.net/11336/8989
dc.description.abstract
Let G be a real reductive Lie group and let τ : G −→ GL(V ) be a real reductive representation of G with (restricted) moment map mg : V {0} −→ g. In this work, we introduce the notion of nice space of a real reductive representation to study the problem of how to determine if a G-orbit is distinguished (i.e. it contains a critical point of the norm squared of mg). We give an elementary proof of the well-known convexity theorem of Atiyah–Guillemin– Sternberg in our particular case and we use it to give an easyto-check sufficient condition for a G-orbit of an element in a nice space to be distinguished. In the case where G is algebraic and τ is a rational representation, the above condition is also necessary (making heavy use of recent results of Michael Jablonski), obtaining a generalization of Nikolayevsky’s nice basis criterion. We also provide useful characterizations of nice spaces in terms of the weights of τ . Finally, some applications to ternary forms are presented.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Elsevier
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dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Real Reductive Representations
dc.subject
Real Reductive Lie Groups
dc.subject
Distinguished Orbits
dc.subject
The Convexity Of the Moment Map
dc.subject.classification
Matemática Pura
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dc.subject.classification
Matemáticas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
On distinguished orbits of reductive representations
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2016-11-25T14:00:14Z
dc.journal.volume
396
dc.journal.pagination
61-81
dc.journal.pais
Países Bajos
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dc.journal.ciudad
Amsterdam
dc.description.fil
Fil: Fernández Culma, Edison Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Centro de Investigación y Estudios de Matemática de Córdoba(p); Argentina. Universidad Nacional de Córdoba; Argentina
dc.journal.title
Journal Of Algebra
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dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0021869313004584
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1016/j.jalgebra.2013.07.031
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1301.4949v1
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