The partition algebra revisited

DOI10.1006/JABR.2000.8365zbMath0974.20013OpenAlexW1984483279MaRDI QIDQ1584614

David B. Wales, William F. IV Doran

Publication date: 28 February 2001

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.2000.8365

zbMATH Keywords

Temperley-Lieb algebrassymmetric groupsBrauer algebraspartition algebrascell modulescellular algebras

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Hecke algebras and their representations (20C08) Representations of finite symmetric groups (20C30) Representations of associative Artinian rings (16G10) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc. (16E60)

Related Items (17)

A new approach to the representation theory of the partition category ⋮ The center of the partition algebra ⋮ Congruence Lattices of Ideals in Categories and (Partial) Semigroups ⋮ On partition algebras for complex reflection groups. ⋮ On blocks of Deligne's category \(\underline {\text{Re}}\text p (S_t)\). ⋮ Multiparameter colored partition category and the product of the reduced Kronecker coefficients ⋮ On the modular representation theory of the partition algebra ⋮ The blocks of the partition algebra in positive characteristic. ⋮ Character orthogonality for the partition algebra and fixed points of permutations ⋮ On the decomposition matrix of the partition algebra in positive characteristic. ⋮ CHARACTERIZATION FOR THE MODULAR PARTY ALGEBRA ⋮ Symmetric functions in noncommuting variables ⋮ Set-partition tableaux and representations of diagram algebras ⋮ Cellular bases for algebras with a Jones basic construction ⋮ Cohomological stratification of diagram algebras. ⋮ Partition algebras. ⋮ Classification of congruences of twisted partition monoids

Cites Work

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• On the decomposition of Brauer's centralizer algebras
• Polynomial representations of \(GL_n\)
• The representation theory of the symmetric groups
• The partition algebras and a new deformation of the Schur algebras
• On the semisimplicity of the Brauer centralizer algebras
• Cellular algebras
• The structure of the partition algebras
• TEMPERLEY-LIEB ALGEBRAS FOR NON-PLANAR STATISTICAL MECHANICS — THE PARTITION ALGEBRA CONSTRUCTION

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