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Centralizers of the infinite symmetric group

SPEAKER: Zajj Daugherty (Dartmouth College)

TITLE: Centralizers of the infinite symmetric group

ABSTRACT: The partition algebra arises as the algebra of operators that commute with the diagonal action of the finite symmetric group S_n on the k-fold tensor product of the n-dimensional permutation module (akin to the classical Schur-Weyl duality between the symmetric group and the general linear group). Recently, this relationship between the symmetric group and the partition algebra has presented itself relevant to the study of several other algebraic topics, such as representation theoretic stability and the study of symmetric functions. In each of these contexts, however, a limit to the infinite symmetric group is taken, and a question arises as to what is the appropriate centralizer algebra. In this talk, I will explore several answers to this question, and how they depend on context. This work is joint with Peter Herbrich.