Weingarten function

In mathematics, Weingarten functions are rational functions indexed by partitions of integers that can be used to calculate integrals of products of matrix coefficients over classical groups. They were first studied by Weingarten (1978) who found their asymptotic behavior, and named by Collins (2003), who evaluated them explicitly for the unitary group. In mathematics, Weingarten functions are rational functions indexed by partitions of integers that can be used to calculate integrals of products of matrix coefficients over classical groups. They were first studied by Weingarten (1978) who found their asymptotic behavior, and named by Collins (2003), who evaluated them explicitly for the unitary group. Weingarten functions are used for evaluating integrals over the unitary group Ud of products of matrix coefficients of the form (Here U ∗ {displaystyle U^{*}} denotes the conjugate transpose of U {displaystyle U} , alternatively denoted as U † {displaystyle U^{dagger }} .)