Averages over classical compact Lie groups and Weyl characters

Paul-Olivier Dehaye

We compute $E_G (\prod_i \tr(g^{λ_i}))$, where $G=Sp(2n)$ or $SO(m)(m=2n,2n+1)$ with Haar measure. This was first obtained by Persi Diaconis and Mehrdad Shahshahani, but our proo…