The character values of the irreducible constituents of a transitive permutation representation
Let \(G\) be a finite group and let \(M\) be a given subgroup of \(G\). The permutation character of \(G\) on \(M\) over the complex field \(\mathbb{C}\) is denoted by \((1_M)^G\). In the paper under review the authors develop a method to find all the irreducible ordinary characters \(\chi_r\) occurring as a constituent of \((1_M)^G\). They also determine the multiplicity of each \(\chi_r\) in \((1_M)^G\). They illustrate the method for Janko's sporadic group \(G=J_1\) and \(M=C_G(z)\), where \(z\) is an involution in \(G\).
scientific article; zbMATH DE number 1798904