The Schur–Weyl graph and Thoma’s theorem

We introduce a graded graph, called the Schur–Weyl graph, which is a covering of the Young graph closely related to the RSK algorithm. Then we explain how it allows one to obtain a new, purely combinatorial, proof of Thoma's theorem, which describes the indecomposable characters of the infinite symmetric group, in the discrete case. Based on joint work with A.M.Vershik.