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- W2167165737 abstract "We review and introduce several approaches to the study of centralizer algebras of the infinite symmetric group $S_{infty}$. Our work is led by the double commutant relationship between finite symmetric groups and partition algebras; in the case of $S_{infty}$, we obtain centralizer algebras that are contained in partition algebras. In view of the theory of symmetric functions in non-commuting variables, we consider representations of $S_{infty}$ that are faithful and that contain invariant elements; namely, non-unitary representations on sequence spaces. Nous étudions les algèbres du centralisateur du groupe symétrique infini $S_{infty}$, passant en revue certaines approches et en introduisant de nouvelles. Notre travail est basé sur la relation du double commutant entre le groupe symétrique fini et les algèbres de partition; dans le cas de $S_{infty}$, nous obtenons des algèbres du centralisateur contenues dans les algèbres de partition. Compte tenu de la théorie des fonctions symétriques en variables non commutatives, nous considérons les représentations de $S_{infty}$ qui sont fidèles et contiennent les invariants; c’est-à-dire, les représentations non unitaires sur les espaces de suites." @default.
- W2167165737 created "2016-06-24" @default.
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- W2167165737 date "2014-01-01" @default.
- W2167165737 modified "2023-09-25" @default.
- W2167165737 title "Centralizers of the infinite symmetric group" @default.
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- W2167165737 doi "https://doi.org/10.46298/dmtcs.2414" @default.
- W2167165737 hasPublicationYear "2014" @default.
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