PublisherThe University of Arizona.
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AbstractThe centralizer algebra of a representation of a finite group G on a complex vector space V is the algebra of all endomorphisms of V that commute with the endomorphisms obtained from the representation. By studying centralizer algebras, we can obtain information about the irreducible representations of G. In general it is not easy to extract meaningful information from the centralizer algebra. However, in the case of a permutation representation there are convenient combinatorial descriptions of the centralizer algebra’s structure. In this thesis, I describe some known methods for investigating these algebras. I also include several functions for performing relevant computations in GAP and examples of their use.