Geodesic
The Schur--Weyl graph and Thoma's theorem.
Funkcionalʹnyj analiz i ego priloženiâ, Tome 55 (2021) no. 3, pp. 26-41.

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We define a graded graph, called the Schur–Weyl graph, which arises naturally when one considers simultaneously the RSK algorithm and the classical duality between representations of the symmetric and general linear groups. As one of the first applications of this graph, we give a new proof of the completeness of the list of discrete indecomposable characters of the infinite symmetric group.
Keywords: Schur–Weyl graph, RSK algorithm, Thoma's theorem, central measures. 
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A. M. Vershik; N. V. Tsilevich. The Schur--Weyl graph and Thoma's theorem.. Funkcionalʹnyj analiz i ego priloženiâ, Tome 55 (2021) no. 3, pp. 26-41. http://geodesic.mathdoc.fr/item/FAA_2021_55_3_a1/

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