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Integration over angular variables for two coupled matrices

Abstract : An integral over the angular variables for two coupled $n$ x $n$ real symmetric, complex hermitian or quaternion self-dual matrices is expressed in term of the eigenvalues and eigenfunctions of a hamiltonian closely related to the Calogero hamiltinian. This generalizes the known result for the complex hermitian matrices. The integral can thus be evaluated for $n = 2$ and reduced to a single sum for $n = 3$
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G. Mahoux, M.L. Mehta, J.-M. Normand. Integration over angular variables for two coupled matrices. Pavel Bleher; Alexander Its. Random Matrix Models and Their Applications, 40, Cambridge UP, pp.301-320, 2001, MSRI Publications, 0-521-80209-1. ⟨cea-02905122⟩

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