TY - JOUR
T1 - On the dimensions of cartesian symmetry classes
AU - Zamani, Yousef
AU - Shahryari, Mohammad
PY - 2012/9
Y1 - 2012/9
N2 - The notion of Cartesian symmetry classes is introduced in [T. G. Lei, Notes on Cartesian symmetry classes and generalized trace functions, Linear Algebra Appl. 292 (1999) 281[288]. In this paper, we discuss these classes and compute the dimensions of these classes in terms of the fixed point character of S m. Also, we give a formula for the dimension of Cartesian symmetry class V χ(G) in terms of the rank of an idempotent matrix M(χ). Some properties of generalized trace functions of a matrix are concluded.
AB - The notion of Cartesian symmetry classes is introduced in [T. G. Lei, Notes on Cartesian symmetry classes and generalized trace functions, Linear Algebra Appl. 292 (1999) 281[288]. In this paper, we discuss these classes and compute the dimensions of these classes in terms of the fixed point character of S m. Also, we give a formula for the dimension of Cartesian symmetry class V χ(G) in terms of the rank of an idempotent matrix M(χ). Some properties of generalized trace functions of a matrix are concluded.
KW - Cartesian symmetry classes
KW - Irreducible characters
KW - generalized trace functions
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U2 - 10.1142/S1793557112500465
DO - 10.1142/S1793557112500465
M3 - Article
AN - SCOPUS:84869143529
SN - 1793-5571
VL - 5
JO - Asian-European Journal of Mathematics
JF - Asian-European Journal of Mathematics
IS - 3
M1 - 1250046
ER -