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SYMMETRY CLASSES OF TENSORS ASSOCIATED TO NONABELIAN GROUPS OF ORDER $pq$

Part of: Basic linear algebra Representation theory of groups

Published online by Cambridge University Press:  16 March 2016

KIJTI RODTES
KIJTI RODTES*
Affiliation:
Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand email kijtir@nu.ac.th
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Abstract

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Necessary and sufficient conditions for the existence of an orthogonal $\ast$-basis of symmetry classes of tensors associated to nonabelian groups of order $pq$ are provided by using vanishing sums of roots of unity.

Keywords

symmetry classes of tensorsorthogonal basisnonabelian groups of order pqvanishing sums of roots of unity

MSC classification

Primary: 20C30: Representations of finite symmetric groups
Secondary: 15A69: Multilinear algebra, tensor products
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 94 , Issue 1 , August 2016 , pp. 36 - 42
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

Berberian, S. K., ‘Non-abelian groups of order pq’, Amer. Math. Monthly 60 (1953), 37–40.Google Scholar
Darafsheh, M. R. and Pournaki, M. R., ‘On the orthogonal basis of the symmetry classes of tensors associated with the dicyclic group’, Linear Multilinear Algebra 47 (2000), 137–149.CrossRefGoogle Scholar
Etingof, P., Golberg, O., Hensel, S., Liu, T., Schwendner, A., Vaintrob, D. and Yudovina, E., Introduction to Representation Theory (MIT Open Courseware, 2011), http://math.mit.edu/ etingof/replect.pdf.Google Scholar
Exoo, G., ‘Some applications of pq-groups in graph theory’, Discuss. Math. Graph Theory 24(1) (2004), 109–114.Google Scholar
Freese, R., ‘Inequalities for generalized matrix functions based on arbitrary characters’, Linear Algebra Appl. 7 (1973), 337–345.Google Scholar
Holmes, R. R., ‘Orthogonality of cosets relative to irreducible character of finite groups’, Linear Multilinear Algebra 52 (2004), 133–143.CrossRefGoogle Scholar
Holmes, R. R. and Kodithuwakku, A., ‘Orthogonal bases of Brauer symmetry classes of tensors for the dihedral group’, Linear Multilinear Algebra 61 (2013), 1136–1147.CrossRefGoogle Scholar
Holmes, R. R. and Tam, T. Y., ‘Symmetry classes of tensors associated with certain groups’, Linear Multilinear Algebra 32 (1992), 21–31.Google Scholar
Hormozi, M. and Rodtes, K., ‘Symmetry classes of tensors associated with the semi-dihedral groups SD 8n ’, Colloq. Math. 131(1) (2013), 59–67.Google Scholar
Lam, T. Y. and Leung, K. H., ‘On vanishing sums of roots of unity’, J. Algebra 224 (2000), 91–109.CrossRefGoogle Scholar
Li, C. K. and Aaharia, A., ‘Induced operators on symmetry classes of tensors’, Trans. Amer. Math. Soc. 354 (2002), 807–836.CrossRefGoogle Scholar
Merris, R., Multilinear Algebra (Gordon and Breach, Amsterdam, 1997).Google Scholar
Poursalavati, N. S., ‘On the symmetry classes of tensors associated with certain Frobenius groups’, Pure Appl. Math. J. 3(1) (2014), 7–10.Google Scholar
Wang, B. Y. and Gong, M. P., ‘A higher symmetry class of tensors with an orthogonal basis of decomposable symmetrized tensors’, Linear Multilinear Algebra 30(1–2) (1991), 61–64.Google Scholar