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Representations and Characters of Groups, Second Edition by Martin Liebeck, Gordon James

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19

Tensor products

The idea of multiplying a character of a group G by a linear character of G was introduced at the end of Chapter 17, and it can be extended to include the product of any pair of characters χ and ψ. The value of the product χψ on an element g of G is simply χ(g)ψ(g). It is therefore straightforward to calculate the product, but a little ingenuity is required in order to justify the conclusion that the product χψ is a character of G. The plan is to take imageG-modules V and W with characters χ and ψ respectively, and to put them together to form a new G-module, called the tensor product of V and W, which has character χψ.

An important ...

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