Induced operators on symmetry classes of polynomials

Document Type: Research Paper

Authors

Sahand University of Technology

Abstract

‎‎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.

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Main Subjects


[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.