Generalized Cartesian symmetry classes

چکیده مقاله

Let $V$ be a unitary space‎. ‎Suppose $G$ is a subgroup of the full symmetric group $S_{m}$ and $\mathfrak{X}$ is an irreducible unitary representation of $G$‎. ‎In this paper‎, ‎we introduce the generalized Cartesian symmetry class over $V$ associated with $G$ and $\mathfrak{X}$‎. ‎Then we investigate some important properties of this vector space‎. ‎Also‎, ‎we study some basic properties of the induced linear operators on the generalized Cartesian symmetry classes‎. ‎Some open problems are also given.‎.