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Abstracts

The concept of data indexed by finite symmetry orbits is reviewed within the data-analytic framework of symmetry studies. Data decompositions are discussed in terms of canonical projections and Plancherel’s formulas, and interpreted in terms of orbit invariants.

irreducible representations; irreducible characters; finite groups; canonical projections; Fourier transforms; convolution

Se revisa el concepto de datos indexados por órbitas simétricas finitas en el marco de estudios de simetría. Se discute la descomposición de datos en términos de proyecciones canónicas y fórmulas de Plancherel, e interpretada en términos de órbitas invariantes.

representaciones irreducibles; características irrducibles; grupos finitos; proyecciones canónicas; transformada de Fourier; convolución

Symmetry orbits and their data-analytic properties

Órbitas de simetría y sus propiedades en análisis de datos

Marlos A.G. Viana^*+

*^{Dirección para correspondencia:}
Abstract

The concept of data indexed by finite symmetry orbits is reviewed within the data-analytic framework of symmetry studies. Data decompositions are discussed in terms of canonical projections and Plancherel’s formulas, and interpreted in terms of orbit invariants.

Keywords: irreducible representations, irreducible characters, finite groups, canonical projections, Fourier transforms, convolution.

Resumen

Se revisa el concepto de datos indexados por órbitas simétricas finitas en el marco de estudios de simetría. Se discute la descomposición de datos en términos de proyecciones canónicas y fórmulas de Plancherel, e interpretada en términos de órbitas invariantes.

Palabras clave: representaciones irreducibles, características irrducibles, grupos finitos, proyecciones canónicas, transformada de Fourier, convolución.

Mathematics Subject Classification: 60B15, 60F05, 05E05.

Contenido disponible en pdf

References

References

[1] Viana, M.; Lakshminarayanan, V. (2013) Dihedral Fourier Analysis: Data-Analytic Aspects and Applications. Lecture Notes in Statistics 206, Springer, New York, N.Y.
[2] Viana, M. (2008) Symmetric Studies: An Introduction to the Analysis of Structured Data in Applications. Cambridge University Press, New York, N.Y.
[3] Weyl, H. (1977) The Classical Groups: Their Invariants and Representations. Princeton University Press, Landmarks in Mathematics and Physics. Original work (1939).

^*Correspondencia a:

Marlos A.G. Viana.

University of Illinois at Chicago Eye Center, Chicago, Illinois, U.S.A. E-Mail: viana@uic.edu

^*University of Illinois at Chicago Eye Center, Chicago, Illinois, U.S.A. E-Mail: viana@uic.edu

Received: 31/Jan/2013; Revised: 17/May/2013; Accepted: 28/May/2013

Publication Dates

Publication in this collection
12 Mar 2014
Date of issue
Dec 2013

History

Received
31 Jan 2013
Reviewed
17 May 2013
Accepted
28 May 2013

[1] References

[1] Viana, M.; Lakshminarayanan, V. (2013) Dihedral Fourier Analysis: Data-Analytic Aspects and Applications. Lecture Notes in Statistics 206, Springer, New York, N.Y.

[2] [2] Viana, M. (2008) Symmetric Studies: An Introduction to the Analysis of Structured Data in Applications. Cambridge University Press, New York, N.Y.

[3] [3] Weyl, H. (1977) The Classical Groups: Their Invariants and Representations. Princeton University Press, Landmarks in Mathematics and Physics. Original work (1939).