Primitive Central Idempotents in Rational Group Algebras

Abstract

A complex irreducible character χ of a finite group G, with an affording representation ρ, is defined to have the property P if, for all g ∈ G, either χ(g) = 0 or all the eigen-values of ρ(g) have the same order. An explicit expression for the primitive central idempotent of the rational group algebra Q [G] associated with a complex irreducible character having the property P is derived. Several consequences are then obtained.