The partition algebras and a new deformation of the Schur algebras

DOI10.1006/jabr.1997.7164zbMath0923.20009OpenAlexW2081919030WikidataQ61847556 ScholiaQ61847556MaRDI QIDQ1265554

David J. Woodcock, Paul P. Martin

Publication date: 9 August 1999

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

Full work available at URL: https://doi.org/10.1006/jabr.1997.7164

zbMATH Keywords

general linear groupsSchur algebrasrepresentationspartition algebrasdecomposition matricesgroup algebras of symmetric groups

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30) Representation theory for linear algebraic groups (20G05) Deformations of associative rings (16S80)

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Cites Work

• Combinatorics and the Schur algebra
• Straightening codeterminants
• Polynomial representations of \(GL_n\)
• The diamond lemma for ring theory
• On central idempotents in the partition algebra
• Algebras in higher-dimensional statistical mechanics -- the exceptional partition (mean field) algebras
• Decomposition numbers for symmetric groups and composition factors of Weyl modules
• The structure of the partition algebras
• TEMPERLEY-LIEB ALGEBRAS FOR NON-PLANAR STATISTICAL MECHANICS — THE PARTITION ALGEBRA CONSTRUCTION
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