# Schur-Weyl duality and large $N$ limit in 2d Yang-Mills theory

Wilson loops are the basic observables of Yang-Mills theory, and their expectation is rigorously defined on the Euclidean plane and on a compact Riemannian surface. Focusing on the case where the structure group is the unitary group $U(N)$, I will present a formula that computes any Wilson loop expectation in almost purely combinatorial terms, thanks to the dictionary between unitary and symmetric quantities provided by the Schur-Weyl duality. This formula should be applicable to the computation of the large $N$ limit of the Wilson loop expectations, also called the master field, and of which the existence on the sphere was proved by Antoine Dahlqvist and James Norris.