A similar formula to the one established by Ansemil and Floret for symmetric tensor products of direct sums is proved for alternating and Jacobian tensor products. It is then applied to stable spaces where a number of isomorphisms between spaces of tensors or multilinear forms are unveiled. A connection between these problems and irreducible group representations is made.
"Tensor products of direct sums." Ark. Mat. 43 (1) 167 - 180, April 2005. https://doi.org/10.1007/BF02383617