[math] \newcommand{\mathds}{\mathbb}[/math]

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Work out estimates for the integrals of type

[[math]] \int_{S_N^+}v_{i_1j_1}v_{i_2j_2}v_{i_3j_3}v_{i_4j_4} [[/math]]

and then for the Weingarten function of [math]S_N^+[/math] at [math]k=4[/math].