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Centralizers of the infinite symmetric group

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.
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Zajj Daugherty, Peter Herbrich. Centralizers of the infinite symmetric group. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.453-464, ⟨10.46298/dmtcs.2414⟩. ⟨hal-01207602⟩

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