Abstract
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.
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This work was supported by the Russian Science Foundation grant no. 21-11-00152.
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Translated from Funktsional'nyi Analiz i ego Prilozheniya, 2021, Vol. 55, pp. 26–41 https://doi.org/10.4213/faa3917.
To the memory of S. V. Kerov (12.06.1946–30.07.2000)
Translated by N. V. Tsilevich
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Vershik, A.M., Tsilevich, N.V. The Schur–Weyl Graph and Thoma’s Theorem. Funct Anal Its Appl 55, 198–209 (2021). https://doi.org/10.1134/S0016266321030023
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DOI: https://doi.org/10.1134/S0016266321030023