Induced operators on symmetry classes of tensors

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.

On the Dimensions of Cyclic Symmetry Classes of Tensors

The dimensions of the symmetry classes of tensors, associated with a certain cyclic subgroup of $m which is generated by a product of disjoint cycles is explicitly given in terms of the generalized Ramanujan sum. These dimensions can also be expressed as the Euler φ-function and the Möbius function.

Symmetry Classes for Even-order Tensors

The purpose of this article is to give a complete and general answer to the recurrent problem in continuum mechanics of the determination of the number and the type of symmetry classes of an even-order tensor space. This kind of investigation was initiated for the space of elasticity tensors. Since then, different authors solved this problem for other kinds of physics such as photoelectricity, ...

Non-Vanishing and Orthogonal Basis of Symmetry Classes of Tensors

By Cayley’s theorem, any finite group G of order n can be regarded as a subgroup of the symmetric group $n. Let χ be any irreducible complex character of G and let V n χ (G) denote the symmetry classes of tensors associated with G and χ. In this paper assuming the Cayley representation of G, we obtain a formula for the dimension of V n χ (G) and discuss its non-vanishing in general. A necessary...

Some equivalence classes of operators on B(H)