# 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.
Title matrix representation MatrixRepresentation 2013-03-22 14:53:56 2013-03-22 14:53:56 drini (3) drini (3) 9 drini (3) Definition msc 20C99 PermutationRepresentation