×

Generalized symmetry classes of tensors. (English) Zbl 07285970

Summary: Let \(V\) be a unitary space. For an arbitrary subgroup \(G\) of the full symmetric group \(S_{m}\) and an arbitrary irreducible unitary representation \(\Lambda\) of \(G\), we study the generalized symmetry class of tensors over \(V\) associated with \(G\) and \(\Lambda\). Some important properties of this vector space are investigated.

MSC:

20C30 Representations of finite symmetric groups
15A69 Multilinear algebra, tensor calculus
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Babaei, E.; Zamani, Y., Symmetry classes of polynomials associated with the dihedral group, Bull. Iran. Math. Soc. 40 (2014), 863-874
[2] Babaei, E.; Zamani, Y., Symmetry classes of polynomials associated with the direct product of permutation groups, Int. J. Group Theory 3 (2014), 63-69
[3] Babaei, E.; Zamani, Y.; Shahryari, M., Symmetry classes of polynomials, Commun. Algebra 44 (2016), 1514-1530
[4] Darafsheh, M. R.; 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
[5] Silva, J. A. Dias da; Torres, M. M., On the orthogonal dimensions of orbital sets, Linear Algebra Appl. 401 (2005), 77-107
[6] Gong, M.-P., Generalized symmetric tensors and related topics, Linear Algebra Appl. 236 (1996), 113-129
[7] Holmes, R. R.; Kodithuwakku, A., Orthogonal bases of Brauer symmetry classes of tensors for the dihedral group, Linear Multilinear Algebra 61 (2013), 1136-1147
[8] Lei, T.-G., Generalized Schur functions and generalized decomposable symmetric tensors, Linear Algebra Appl. 263 (1997), 311-332
[9] Marcus, M., Finite Dimensional Multilinear Algebra. Part I, Pure and Applied Mathematics 23, Marcel Dekker, New York (1973)
[10] Merris, R., Multilinear Algebra, Algebra, Logic and Applications 8, Gordon and Breach, Langhorne (1997)
[11] Ranjbari, M.; Zamani, Y., Induced operators on symmetry classes of polynomials, Int. J. Group Theory 6 (2017), 21-35
[12] Shahryari, M., On the orthogonal bases of symmetry classes, J. Algebra 220 (1999), 327-332
[13] Shahryari, M.; Zamani, Y., Symmetry classes of tensors associated with Young subgroups, Asian-Eur. J. Math. 4 (2011), 179-185
[14] Zamani, Y., On the special basis of a certain full symmetry class of tensors, PU.M.A., Pure Math. Appl. 18 (2007), 357-363
[15] Zamani, Y.; Babaei, E., The dimensions of cyclic symmetry classes of polynomials, J. Algebra Appl. 13 (2014), Article ID 1350085, 10 pages
[16] Zamani, Y.; Ranjbari, M., Representations of the general linear group over symmetry classes of polynomials, Czech. Math. J. 68 (2018), 267-276
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.