Definition 3

Let $\varrho$ be a finite-dimensional unitary representation of G in a Hilbert space E. Let $k$ be a positive integer. The absolute moment of order $2k$ of $\varrho$ is defined to be, and is denoted by $M_{2k}(\varrho )$, the dimension of the subspace of G-invariant elements in the representation $\overline{\varrho}^{\otimes k}\otimes \varrho^{\otimes k}$.