Séminaire Lotharingien de Combinatoire, 91B.50 (2024), 12 pp.

Rosa Orellana, Nancy Wallace and Mike Zabrocki

Quasipartition and Planar Quasipartition Algebras

Abstract. The quasi-partition algebras were introduced by Daugherty and the first author in 2014, as centralizers of the symmetric group. Here we provide a more general construction using idempotents which allows us to define the half quasi-partition algebra. Our construction allows us to describe the planar analogues of these quasi-partition algebras. In this case the planar subalgebras are centralizer algebras of the quantum group U_q(sl₂) and of dimensions equal to Motzkin and Riordan numbers. We use a Bratteli-like diagram to describe how the representation theories of these algebras are related.

Received: November 15, 2023. Accepted: February 15, 2024. Final version: April 1, 2024.

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