Séminaire Lotharingien de Combinatoire, 82B.58 (2019), 12 pp.

Tom Halverson

Set-partition tableaux, symmetric group multiplicities, and partition algebra modules

Abstract. Set-partition tableaux are Young tableaux whose boxes are filled with the blocks of a set partition. We use them to compute multiplicities of symmetric group modules in tensor product representations and to index bases of irreducible modules of the partition algebra. We give an action of the partition algebra on this basis analogous to Young's natural representation of the symmetric group. This action restricts to give natural representations for subalgebras of the partition algebra including the Brauer, Temperley-Lieb, rook-monoid, and Motzkin algebras.


Received: November 15, 2018. Accepted: February 17, 2019. Final version: April 1, 2019.

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