On the restrict-induce map of group characters
D. L. Winter · Proceedings of the American Mathematical Society · 1968
The purpose of this note is to give a new proof of the following theorem due to E. Artin. Theorem.Each ordinary irreducible character 0/ a finite group is a linear combination with rational coefficients 0/ characters induced from linear characters of cyclic subgroups.Let G be a finite group and let Kx, ■ ■ ■ , Kn be the classes of conjugate elements of G. Then the ordinary irreducible characters xi.* ' • 1 Xn form a basis of the vector space U of all complex-valued class functions on G over the complex number field.This basis is orthonormal relative to the usual inner product.There is another orthonormal basis ai, • ■ ■ , an defined by