Elements of Representation Theory

Abstract

Let G be a group. A group D of square matrices of order n which is homomorphic to G is said to provide an n-dimensional linear representation or a matrix representation of G. One usually calls it simply a representation of G. Thus, if g₁ → A_g1, g₂ → A_g2 under the mapping where g₁, g₂ ∈ G and A_g1 A_g2 ∈ D, we demand that

$${g_1}{g_2} \to {A_{g1}}{A_{g2}}$$

((4.1.1))

.