Zajj Daugherty ; Peter Herbrich - Centralizers of the infinite symmetric group

dmtcs:2414 - Discrete Mathematics & Theoretical Computer Science, January 1, 2014, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) - https://doi.org/10.46298/dmtcs.2414
Centralizers of the infinite symmetric groupArticle

Authors: Zajj Daugherty 1; Peter Herbrich 1

  • 1 Department of Mathematics [Dartmouth]

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.


Volume: DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Section: Proceedings
Published on: January 1, 2014
Imported on: November 21, 2016
Keywords: representation theory,infinite symmetric group,centralizer algebras,partition algebras,symmetric functions,Banach spaces,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]
Funding:
    Source : OpenAIRE Graph
  • Combinatorics and representation theory of centralizer algebras; Funder: National Science Foundation; Code: 1162010

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