Geodesic
The comments to the article by Elmar Thoma: ``Die unzerlegbaren, positiv-definiten Klassenfunktionen der abz \"ahlbar unendlichen, symmetrischen Gruppe''
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXV, Tome 528 (2023), pp. 37-46

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We comment here the classical article by Elmar Thoma abour caracters of the infinite symmetric group; consider the proof of the main result , which compare with the following papers of different authors who suggested various approves to the theory of the characters and representations of that group as well as related groups. 
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     author = {A. M. Vershik},
     title = {The comments to the article by {Elmar} {Thoma:} {``Die} unzerlegbaren, positiv-definiten {Klassenfunktionen} der abz \"ahlbar unendlichen, symmetrischen {Gruppe''}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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A. M. Vershik. The comments to the article by Elmar Thoma: ``Die unzerlegbaren, positiv-definiten Klassenfunktionen der abz \"ahlbar unendlichen, symmetrischen Gruppe''. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXV, Tome 528 (2023), pp. 37-46. http://geodesic.mathdoc.fr/item/ZNSL_2023_528_a1/