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A method for computing integrals of polynomial functions on compact symmetric spaces is given.
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R. Goodman and N. R. Wallach, Symmetry, representations, and invariants, Graduate Texts in Mathematics 255
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S. Matsumoto and J. Novak, Jucys-Murphy elements and unitary matrix integrals, International Mathematics Research Notices (2013), no. 2, 362–397
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