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We give a Fourier-type formula for computing the orthogonal Weingarten formula.
Don Weingarten, Asymptotic behavior of group integrals in the limit of infinite rank, J. Mathematical Phys., 19
1918
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A. M. Parkhurst and A. T. James, Zonal polynomials of order 1 through 12, Selected tables in mathematical statistics, vol. 2, (1974), 199-388
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I. G. Macdonald, Symmetric Functions and Hall Polynomials, second ed., Oxford University Press, Oxford, 1995
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M. Petkovsek, H. Wilf and D. Zeilberger, A=B, Ltd., Wellesley, MA, 1996
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R. Goodman and N. Wallach, Representations and invariants of the classical groups, Cambridge University Press, Cambridge, 1998
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B. Collins, Moments and cumulants of polynomial random variables on unitary groups, the Itzykson-Zuber integral, and free probability, Int. Math. Res. Not. 17
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B. Collins and P. Śniady, Integration with respect to the Haar measure on unitary, orthogonal and symplectic group, Comm. Math. Phys. 264
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T. Banica and B. Collins, Integration over compact quantum groups, Publ. RIMS 43
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J. Novak, Truncations of random unitary matrices and Young tableaux, Electoronic J. Combi. 14
2007
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B. Collins and M. Stolz, Borel theorems for random matrices from the classical compact symmetric spaces, The Annals of Probability 36
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S. Matsumoto and J. Novak, In preparation, 2009
2009
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