Geodesic
Description of the evolution of finite-dimensional quantum systems by permutation groups
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXV, Tome 528 (2023), pp. 134-152

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We consider constructive approaches to quantum theory: quantum \break mechanics based on permutation representations of finite groups and the Weyl–Schwinger finite phase space quantum mechanics. We show that both approaches lead to the conclusion that, at a deep level, quantum evolution is based on permutations of finite sets. 
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     author = {V. V. Kornyak},
     title = {Description of the evolution of finite-dimensional quantum systems by permutation groups},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {134--152},
     publisher = {mathdoc},
     volume = {528},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2023_528_a8/}
}
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V. V. Kornyak. Description of the evolution of finite-dimensional quantum systems by permutation groups. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXV, Tome 528 (2023), pp. 134-152. http://geodesic.mathdoc.fr/item/ZNSL_2023_528_a8/