Unitary Representations of Groups, Duals, and Characters Katharine Manasco The popular notion of a

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Unitary Representations of Groups, Duals, and Characters Katharine Manasco The popular notion of aUnitary representations of groups play an important role in many subjects, including number theory, geometry, probability theory, partial differential equations, and quantum mechanics. This monograph focuses on dual spaces associated to a group, which are spaces of building blocks of general unitary representations. Special attention is paid to discrete groups for which the unitary dual, the most common dual space, has proven to be not useful in