matrix representation

A matrix representation of a group $G$ is a group homomorphism between $G$ and $GL_{n}(\\mathbbmss{C})$ , that is, a function

X:G\\to GL_{n}(\\mathbbmss{C})

such that

•
$X(gh)=X(g)X(h)$ ,
•
$X(e)=I$

Notice that this definition is equivalent to the group representation definition when the vector space $V$ is finite dimensional over $\\mathbbmss{C}$ . The parameter $n$ (or in the case of a group representation, the dimension of $V$ ) is called the degree of the representation.

References

1 Bruce E. Sagan. The Symmetric Group: Representations, Combinatorial Algorithms and Symmetric Functions. 2a Ed. 2000. Graduate Texts in Mathematics. Springer.