The orthogonal Weingarten formula in compact form

الأصل · EN

We present a compact formulation of the orthogonal Weingarten formula, with the traditional quantity I(i₁,...,i₂ₖ:j₁,...,j₂ₖ) = ∫ₒₙuᵢ₁ⱼ₁... uᵢ₂ₖⱼ₂ₖ du replaced by the more advanced quantity I(a)=∫ₒₙΠuijaij du, depending on a matrix of exponents a∈ Mₙ(N). Among consequences, we establish a number of basic facts regarding the integrals I(a): vanishing conditions, possible poles, asymptotic behavior.