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Keywords:
irreducible character; generalized Schur function; orthogonal basis; symmetry class of tensors
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.
References:
[1] Babaei, E., Zamani, Y.: Symmetry classes of polynomials associated with the dihedral group. Bull. Iran. Math. Soc. 40 (2014), 863-874. MR 3255403 | Zbl 1338.05271
[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. DOI 10.22108/ijgt.2014.5479 | MR 3213989 | Zbl 1330.05159
[3] Babaei, E., Zamani, Y., Shahryari, M.: Symmetry classes of polynomials. Commun. Algebra 44 (2016), 1514-1530. DOI 10.1080/00927872.2015.1027357 | MR 3473866 | Zbl 1338.05272
[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. DOI 10.1080/03081080008818639 | MR 1760506 | Zbl 0964.20006
[5] Silva, J. A. Dias da, Torres, M. M.: On the orthogonal dimensions of orbital sets. Linear Algebra Appl. 401 (2005), 77-107. DOI 10.1016/j.laa.2003.11.005 | MR 2133276 | Zbl 1077.15025
[6] Gong, M.-P.: Generalized symmetric tensors and related topics. Linear Algebra Appl. 236 (1996), 113-129. DOI 10.1016/0024-3795(94)00136-7 | MR 1375609 | Zbl 0846.15012
[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. DOI 10.1080/03081087.2012.729583 | MR 3175352 | Zbl 1279.15021
[8] Lei, T.-G.: Generalized Schur functions and generalized decomposable symmetric tensors. Linear Algebra Appl. 263 (1997), 311-332. DOI 10.1016/S0024-3795(96)00542-3 | MR 1453977 | Zbl 0894.15015
[9] Marcus, M.: Finite Dimensional Multilinear Algebra. Part I. Pure and Applied Mathematics 23, Marcel Dekker, New York (1973). MR 0352112 | Zbl 0284.15024
[10] Merris, R.: Multilinear Algebra. Algebra, Logic and Applications 8, Gordon and Breach, Langhorne (1997). DOI 10.1201/9781498714907 | MR 1475219 | Zbl 0892.15020
[11] Ranjbari, M., Zamani, Y.: Induced operators on symmetry classes of polynomials. Int. J. Group Theory 6 (2017), 21-35. DOI 10.22108/ijgt.2017.12406 | MR 3621030
[12] Shahryari, M.: On the orthogonal bases of symmetry classes. J. Algebra 220 (1999), 327-332. DOI 10.1006/jabr.1999.7932 | MR 1714132 | Zbl 0935.15024
[13] Shahryari, M., Zamani, Y.: Symmetry classes of tensors associated with Young subgroups. Asian-Eur. J. Math. 4 (2011), 179-185. DOI 10.1142/S1793557111000150 | MR 2775162 | Zbl 1211.15034
[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. MR 2481889 | Zbl 1212.15053
[15] Zamani, Y., Babaei, E.: The dimensions of cyclic symmetry classes of polynomials. J. Algebra Appl. 13 (2014), Article ID 1350085, 10 pages. DOI 10.1142/S0219498813500850 | MR 3119646 | Zbl 1290.05156
[16] Zamani, Y., Ranjbari, M.: Representations of the general linear group over symmetry classes of polynomials. Czech. Math. J. 68 (2018), 267-276. DOI 10.21136/CMJ.2017.0458-16 | MR 3783598 | Zbl 06861580
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