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Babaei, Esmaeil, Zamani, Yousef. (1393). Symmetry classes of polynomials associated with the direct product of permutation groups. , 3(4), 63-69. doi: 10.22108/ijgt.2014.5479
Esmaeil Babaei; Yousef Zamani. "Symmetry classes of polynomials associated with the direct product of permutation groups". , 3, 4, 1393, 63-69. doi: 10.22108/ijgt.2014.5479
Babaei, Esmaeil, Zamani, Yousef. (1393). 'Symmetry classes of polynomials associated with the direct product of permutation groups', , 3(4), pp. 63-69. doi: 10.22108/ijgt.2014.5479
Babaei, Esmaeil, Zamani, Yousef. Symmetry classes of polynomials associated with the direct product of permutation groups. , 1393; 3(4): 63-69. doi: 10.22108/ijgt.2014.5479

Symmetry classes of polynomials associated with the direct product of permutation groups

International Journal of Group Theory
مقاله 9، دوره 3، شماره 4، اسفند 2014، صفحه 63-69    اصل مقاله (282.05 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2014.5479
نویسندگان
Esmaeil Babaei1؛ Yousef Zamani* 2
1Sahand University of technology
2Sahand University of Technology
چکیده
‎Let $G_{i} $ be a subgroup of $ S_{m_{i}}‎ ,‎\ 1 \leq i \leq k$‎. ‎Suppose $\chi_{i}$ is an irreducible complex character of $G_{i}$‎. ‎We consider $ G_{1}\times \cdots \times G_{k} $ as subgroup of $ S_{m} $‎, ‎where $ m=m_{1}+\cdots‎ +‎m_{k} $‎. ‎In this paper‎, ‎we give a formula for the dimension of $H_{d}(G_{1}\times \cdots \times G_{k}‎, ‎\chi_{1}\times\cdots \times \chi_{k})$ and investigate the existence of an o-basis of this type of classes‎.
کلیدواژه‌ها
Symmetric polynomials؛ symmetry class of polynomials‎؛ ‎orthogonal basis؛ ‎permutaion groups‎؛ ‎complex characters
مراجع
E. Babaei and Y. Zamani Symmetry classes of polynomials associated with the dihedral group to appear in Bull. Iranian Math. Soc.
M. R. Darafsheh and M. R. Pournaki (2000) On the orthogonal basis of the symmetry classes of tensors associated with the dicyclic group Linear and Multilinear Algebra 47, 137-149
M. R. Darafsheh and N. S. Poursalavati (2001) On the existence of the orthogonal basis of the symmetry classes of tensors associated with certain groups SUT J. Math. 37, 1-17
R. R. Holmes (1995) Orthogonal bases of symmetrized tensor spaces Linear and Multilinear Algebra 39, 241-243
I. M. Isaacs (1976) Character Theory of Finite Groups Academic Press, New York
R. Merris (1997) Multilinear Algebra Gordon and Breach Science Publisher, Amsterdam
M. Shahryari (2010) Relative symmetric polynomials Linear Algebra Appl. 433, 1410-1421
M. Shahryari (1999) On the orthogonal bases of symmetry classes J. Algebra 220, 327-332
M. Shahryari and Y. Zamani (2011) Symmetry classes of tensors associated with Young subgroups Asian-Eur. J. Math. 4, 179-185
Y. Zamani and E. Babaei (2014) The dimensions of cyclic symmetry classes of polynomials J. Algebra Appl., (10 pages) 13
Y. Zamani (2007) On the special basis of a certain full symmetry class of tensors Pure Math. Appl. 18, 357-363
Y. Zamani and E. Babaei (2013) Symmetry classes of polynomials associated with the dicyclic group Asian-Eur. J. Math., (10 pages) 6
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