Supercuspidal blocks and the local Langlands correspondence

Let $G$ be a connected reductive group defined over a non-archimedean local field $F$, and let $\mathrm{Rep}^{\mathfrak{s}}(G(F))$ be a supercuspidal Bernstein block. In this paper, we define a cohomology class $[μ_{\mathfrak{s}}]$ represented by a 2-cocycle that encodes the equivalence class of $\m