A Direct Proof of Minkwitz’s Extension Theorem

Let s be an ordinary irreducible character of the finite group G whose restriction m to the subgroup H is irreducible. If F is a d-dimensional matrix representation of CH affording m then by Schur’s Lemma F extends uniquely to an irreducible representation D of CG affording s. The goal of this note is to present a direct proof of Minkwitz’s Theorem [Mink] which gives an explicit formula for D in terms of F and s. (Throughout this note we keep the above notation.)