We show that the symmetry classes of torsion-free covariant derivatives ∇T of r-times covariant tensor fields T can be characterized by LittlewoodRichardson products σ[1] where σ is a representation of the symmetric group Sr which is connected with the symmetry class of T . If σ ∼ [λ] is irreducible then σ[1] has a multiplicity free reduction [λ][1] ∼ ∑ λ⊂μ[μ] and all primitive idempotents belo...

We describe three MATLAB classes for manipulating tensors in order to allow fast algorithm prototyping. A tensor is a multidimensional or N -way array. We present a tensor class for manipulating tensors which allows for tensor multiplication and “matricization.” We have further added two classes for representing tensors in decomposed format: cp tensor and tucker tensor. We demonstrate the use o...

In this paper we introduce three new classes of nonnegative forms (or equivalently, symmetric tensors) and their extensions. The newly identified nonnegative symmetric tensors constitute distinctive convex cones in the space of general symmetric tensors (order 6 or above). For the special case of quartic forms, they collapse into the set of convex quartic homogeneous polynomial functions. We di...

We present the complete gauged N = 4 (half-maximal) supergravities in four and five spacetime dimensions coupled to an arbitrary number of vector mul-tiplets. The gaugings are parameterized by a set of appropriately constrained constant tensors, which transform covariantly under the global symmetry groups SL(2) × SO(6, n) and SO(1, 1) × SO(5, n), respectively. In terms of these tensors the univ...