Characters of wreath products and some applications to representation theory and combinatorics

AbstractThe salient point arising out of a consideration of some seemingly independent topics in representation theory, combinatorics and the theory of numerical polynomials turns out to be a result involving characters of representations of wreath products. The topics are: symmetrized inner products of representations, irreducible characters of wreath products, Frobenius' formula for the irreducible ordinary characters of symmetric groups, the Pólya-Redfield theory of enumeration under group action in combinatorics and results of Rudvalis and Snapper that certain polynomials arising from generalized cycleindices of permutation groups are numerical