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Title: Generalized symmetry classes of tensors (English)
Author: Rafatneshan, Gholamreza
Author: Zamani, Yousef
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 70
Issue: 4
Year: 2020
Pages: 921-933
Summary lang: English
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Category: math
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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. (English)
Keyword: irreducible character
Keyword: generalized Schur function
Keyword: orthogonal basis
Keyword: symmetry class of tensors
MSC: 15A69
MSC: 20C30
idZBL: 07285970
idMR: MR4181787
DOI: 10.21136/CMJ.2020.0044-19
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Date available: 2020-11-18T09:41:45Z
Last updated: 2023-01-02
Stable URL: http://hdl.handle.net/10338.dmlcz/148402
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Reference: [1] Babaei, E., Zamani, Y.: Symmetry classes of polynomials associated with the dihedral group.Bull. Iran. Math. Soc. 40 (2014), 863-874. Zbl 1338.05271, MR 3255403
Reference: [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. Zbl 1330.05159, MR 3213989, 10.22108/ijgt.2014.5479
Reference: [3] Babaei, E., Zamani, Y., Shahryari, M.: Symmetry classes of polynomials.Commun. Algebra 44 (2016), 1514-1530. Zbl 1338.05272, MR 3473866, 10.1080/00927872.2015.1027357
Reference: [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. Zbl 0964.20006, MR 1760506, 10.1080/03081080008818639
Reference: [5] Silva, J. A. Dias da, Torres, M. M.: On the orthogonal dimensions of orbital sets.Linear Algebra Appl. 401 (2005), 77-107. Zbl 1077.15025, MR 2133276, 10.1016/j.laa.2003.11.005
Reference: [6] Gong, M.-P.: Generalized symmetric tensors and related topics.Linear Algebra Appl. 236 (1996), 113-129. Zbl 0846.15012, MR 1375609, 10.1016/0024-3795(94)00136-7
Reference: [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. Zbl 1279.15021, MR 3175352, 10.1080/03081087.2012.729583
Reference: [8] Lei, T.-G.: Generalized Schur functions and generalized decomposable symmetric tensors.Linear Algebra Appl. 263 (1997), 311-332. Zbl 0894.15015, MR 1453977, 10.1016/S0024-3795(96)00542-3
Reference: [9] Marcus, M.: Finite Dimensional Multilinear Algebra. Part I.Pure and Applied Mathematics 23, Marcel Dekker, New York (1973). Zbl 0284.15024, MR 0352112
Reference: [10] Merris, R.: Multilinear Algebra.Algebra, Logic and Applications 8, Gordon and Breach, Langhorne (1997). Zbl 0892.15020, MR 1475219, 10.1201/9781498714907
Reference: [11] Ranjbari, M., Zamani, Y.: Induced operators on symmetry classes of polynomials.Int. J. Group Theory 6 (2017), 21-35. MR 3621030, 10.22108/ijgt.2017.12406
Reference: [12] Shahryari, M.: On the orthogonal bases of symmetry classes.J. Algebra 220 (1999), 327-332. Zbl 0935.15024, MR 1714132, 10.1006/jabr.1999.7932
Reference: [13] Shahryari, M., Zamani, Y.: Symmetry classes of tensors associated with Young subgroups.Asian-Eur. J. Math. 4 (2011), 179-185. Zbl 1211.15034, MR 2775162, 10.1142/S1793557111000150
Reference: [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. Zbl 1212.15053, MR 2481889
Reference: [15] Zamani, Y., Babaei, E.: The dimensions of cyclic symmetry classes of polynomials.J. Algebra Appl. 13 (2014), Article ID 1350085, 10 pages. Zbl 1290.05156, MR 3119646, 10.1142/S0219498813500850
Reference: [16] Zamani, Y., Ranjbari, M.: Representations of the general linear group over symmetry classes of polynomials.Czech. Math. J. 68 (2018), 267-276. Zbl 06861580, MR 3783598, 10.21136/CMJ.2017.0458-16
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