Some relative character theory (Q1346189)

Let \(G\) be a finite group, \(H\) be a subgroup of \(G\) and \(A\) be the ring of integers of a number field \(K\). The main object of the paper is the \(A\)-algebra \(C_0(G,H)\) of \(H\)-class functions of \(G\). For a suitable cyclotomic field \(K\), \(C_0(G,H)\) contains an orthonormal basis. This is the main result of the paper. The well-known Brauer induction theorem is a consequence of this result. Earlier the author got the result in the case when \(G\) is the symmetric group and \(H\) is a Young subgroup.