A seminormal form for partition algebras

DOI10.1016/j.jcta.2013.06.001zbMath1314.05219arXiv1102.2047OpenAlexW1997793461MaRDI QIDQ2349201

John Enyang

Publication date: 19 June 2015

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.2047

zbMATH Keywords

Gram determinantscellular algebrapartition algebraJucys-Murphy elementseminormal form

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30) Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15)

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A new approach to the representation theory of the partition category ⋮ The center of the partition algebra ⋮ Presentations for rook partition monoids and algebras and their singular ideals ⋮ Diagram monoids and Graham-Houghton graphs: idempotents and generating sets of ideals ⋮ Semi-simplicity of Temperley-Lieb algebras of type D ⋮ The blocks of the partition algebra in positive characteristic. ⋮ Irreducible calibrated representations of periplectic Brauer algebras and hook representations of the symmetric group ⋮ Defining an affine partition algebra ⋮ Quantum walled Brauer algebra: commuting families, Baxterization, and representations ⋮ Jucys-Murphy elements and a presentation for partition algebras. ⋮ On representation theory of partition algebras for complex reflection groups ⋮ Set-partition tableaux and representations of diagram algebras ⋮ Cellular bases for algebras with a Jones basic construction ⋮ Howe duality of the symmetric group and a multiset partition algebra

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