Ranjbari, M., Zamani, Y. (2017). Induced operators on symmetry classes of polynomials. International Journal of Group Theory, 6(2), 21-35. doi: 10.22108/ijgt.2017.12406
Mahin Ranjbari; Yousef Zamani. "Induced operators on symmetry classes of polynomials". International Journal of Group Theory, 6, 2, 2017, 21-35. doi: 10.22108/ijgt.2017.12406
Ranjbari, M., Zamani, Y. (2017). 'Induced operators on symmetry classes of polynomials', International Journal of Group Theory, 6(2), pp. 21-35. doi: 10.22108/ijgt.2017.12406
Ranjbari, M., Zamani, Y. Induced operators on symmetry classes of polynomials. International Journal of Group Theory, 2017; 6(2): 21-35. doi: 10.22108/ijgt.2017.12406
Induced operators on symmetry classes of polynomials
In this paper, we give a necessary and sufficient condition for the equality of two symmetrized decomposable polynomials. Then, we study some algebraic and geometric properties of the induced operators over symmetry classes of polynomials in the case of linear characters.
[1] E. Babaei and Y. Zamani, Symmetry classes of polynomials associated with the direct product of permutation groups, Int. J. Group Theory, 3 no. 4 (2014) 63–69.
[2] E. Babaei and Y. Zamani, Symmetry classes of polynomials associated with the dihedral group, Bull. Iranian Math. Soc., 40 no. 4 (2014) 863–874.
[3] E. Babaei, Y. Zamani and M. Shahryari, Symmetry classes of polynomials, Comm. Algebra, 44 (2016) 1514–1530.
[4] R. Bhatia, Positive Definite Matrices, Princeton University Press, 2007.
[5] R. Bhatia and J. A. Dias da Silva, Variation of induced linear operators, Linear Algebra Appl., 341 (2002) 391–402.
[6] H. F. da Cruz and J. A. Dias da Silva, Equality of immanantal decomposable tensors, Linear Algebra Appl., 401 (2005) 29–46.
[7] H. F. da Cruz and J. A. Dias da Silva, Equality of immanantal decomposable tensors, II, Linear Algebra Appl., 395 (2005) 95-119.
[8] I. M. Isaacs, Character Theory of Finite Groups, Corrected reprint of the 1976 original, Academic Press, New York, Dover Publications, Inc., New York, 1994.
[9] M. Marcus, Finite Dimensional Multilinear Algebra, Part I, Pure and Applied Mathematics, 23, Marcel Dekker, Inc., New York, 1973.
[10] R. Merris, Multilinear Algebra, Gordon and Breach Science Publisher, Amsterdam, 1997.
[11] K. Rodtes, Symmetry classes of polynomials assosiated to the semidihedral group and o-basis, J. Algebra Appl., 13 (2014) pp. 7.
[12] M. Shahryari, Relative symmetric polynomials, Linear Algebra Appl., 433 (2010) 1410–1421.
[13] Y. Zamani and E. Babaei, Symmetry classes of polynomials associated with the dicyclic group, Asian-Eur. J. Math., 6 (2013) pp. 10.
[14] Y. Zamani and E. Babaei, The dimensions of cyclic symmetry classes of polynomials, J. Algebra Appl., 13 (2014) pp. 10.
[15] Y. Zamani and M. Ranjbari, Induced operators on the space of homogeneous polynomials, Asian-Eur. J. Math., 9 (2016) pp. 15.