 \langle \Psi^{[\mu]}(\Lambda) | \mathcal{H} | \Psi^{[\mu]}(\Lambda) \rangle =  \sum_{\ell_0 = 0}^{L} \langle \Psi^{[\mu]}(\Lambda) | H_{\ell_0 + 0, \ldots, \ell_0 + \nu}  | \Psi^{[\mu]}(\Lambda) \rangle