ON THE DIMENSIONS OF CARTESIAN SYMMETRY CLASSES
Yousef Zamani, M. Shahryari · Asian-European Journal of Mathematics · 2012
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 Sm. Also, we give a formula for the dimension of Cartesian symmetry class Vχ(G) in terms of the rank of an idempotent matrix M(χ). Some properties of generalized trace functions of a matrix are concluded.