Representation Tensor Product

The vector space tensor product V tensor W of two group representations of a group G is also a representation of G. An element g of G acts on a basis element v tensor w by

 g(v tensor w)=gv tensor gw.

If G is a finite group and V is a faithful representation, then any representation is contained in  tensor ^nV for some n. If V_1 is a representation of G_1 and V_2 is a representation of G_2, then V_1 tensor V_2 is a representation of G_1×G_2, called the external tensor product. The regular tensor product is a special case, with the diagonal embedding of G in G×G.

See also

External Tensor Product, Group, Group Representation, Irreducible Representation, Vector Space, Vector Space Tensor Product

This entry contributed by Todd Rowland

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Rowland, Todd. "Representation Tensor Product." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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