$\nabla_{N(K)}\text{-}\deg({\mathcal{A}}_{|{\mathcal{H}}'_k}(\cdot,\lambda), B({\mathcal{H}}'_k))= \nabla_{N(K)}\text{-}\deg(-{\operatorname{Id}}, B({\mathbb{V}}_{-\Delta}(\mu_k)^K\ominus{\mathbb{V}}_{-\Delta}(\mu_k)^G))