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
Canonical name	MatrixRepresentation
Date of creation	2013-03-22 14:53:56
Last modified on	2013-03-22 14:53:56
Owner	drini (3)
Last modified by	drini (3)
Numerical id	9
Author	drini (3)
Entry type	Definition
Classification	msc 20C99
Related topic	PermutationRepresentation