Cellular subalgebras of the partition algebra
Travis Scrimshaw
Hokkaido University, Sapporo, Japan
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Abstract
We describe various diagram algebras and their representation theory using cellular algebras of Graham and Lehrer and the decomposition into half diagrams. In particular, we show the diagram algebras surveyed here are all cellular algebras and parameterize their cell modules. We give a new construction to build new cellular algebras from a general cellular algebra and subalgebras of the rook Brauer algebra that we call the cellular wreath product.
Cite this article
Travis Scrimshaw, Cellular subalgebras of the partition algebra. J. Comb. Algebra 8 (2024), no. 1/2, pp. 147–207
DOI 10.4171/JCA/84