Group Representations and Harmonic Analysis on Groups

Abstract

By a representation of a group G in a linear space £ over a field κ (the space of the representation) we shall mean a homomorhism T: G → GL(£, κ), where GL(£, κ) is the group of non-singular linear transformations of £. Thus, T is a mapping of G into GL(£, κ) satisfying the conditions

• a) T(g₁g₂) = T(g₁)T(g₂), (1)

• b) T(e) = E, (2) where E is the identity operator in £.