Inmathematics, thetensor representations of thegeneral linear group are those that are obtained by taking finitely manytensor products of thefundamental representation and its dual. The irreducible factors of such a representation are also called tensor representations, and can be obtained by applyingSchur functors (associated toYoung tableaux). These coincide with therational representations of the general linear group.

More generally, amatrix group is any subgroup of the general linear group. A tensor representation of a matrix group is any representation that is contained in a tensor representation of the general linear group. For example, theorthogonal group O(n) admits a tensor representation on the space of all trace-free symmetric tensors of order two. For orthogonal groups, the tensor representations are contrasted with thespin representations.

• Roe Goodman; Nolan Wallach (2009),Symmetry, representations, and invariants, Springer, chapters 9 and 10.
• Bargmann, V., &Todorov, I. T. (1977). Spaces of analytic functions on a complex cone as carriers for the symmetric tensor representations of SO(n). Journal of Mathematical Physics, 18(6), 1141–1148.

• Tensors