In this paper, we compute all the moments of the real Wishart distribution. To do so, we use the Gelfand pair (S2k,H), where H is the hyperoctahedral group, the representation theory of H and some techniques based on graphs.
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Graczyk, P., Letac, G. & Massam, H. The Hyperoctahedral Group, Symmetric Group Representations and the Moments of the Real Wishart Distribution. J Theor Probab 18, 1–42 (2005). https://doi.org/10.1007/s10959-004-0579-9
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DOI: https://doi.org/10.1007/s10959-004-0579-9