Generalizations of some integrals over the unitary group

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Using the character expansion method, we generalize several well-known integrals over the unitary group to the case where general complex matrices appear in the integrand. These integrals are of interest in the theory of random matrices and may also find applications in lattice gauge theory.
6 pages, some references added, version to appear in J. Phys. A: Special Issue on Random Matrix Theory

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