Representations of Permutation Groups |
Contents
Characters of wreath products | 3 |
An application to representation theory Symme | 62 |
An application to combinatorics The theory | 103 |
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a₁ algebraically closed apply basis group beads of colour Bruijn Burnside's lemma character table combinatorics complete system conjugacy classes conjugates corollary cycle-index cyclic factor decomposition matrix defined denotes dimension double cosets elements enumeration problems enumeration theorem equal evaluate f(rik finite group following holds G and H G₁ group G Hence idempotent identity representation inertia group irreducible constituents K-representation lemma Littlewood Math matrix representation natural number necklace normal subgroup number of orbits number of types obtain ordinary irreducible representations ordinary representation pairwise inequivalent permutation character permutation group permutation representation Pólya polynomial Proof rational integral representation of G representation theory respect S-functions selfassociated sentation splitting symmetric groups symmetrized inner products system of pairwise transitive types of graphs underlying vector space V₁ vector space Weyl groups wreath products yields