Alternating submodules for partition algebras, rook algebras, and rook-Brauer algebras

DOI10.1016/j.jpaa.2023.107452OpenAlexW4366783577MaRDI QIDQ6132825

John Maxwell Campbell

Publication date: 17 August 2023

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2023.107452

zbMATH Keywords

partition algebrasalternating submodulesrook algebras

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of orders, lattices, algebras over commutative rings (16G30) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60)

Cites Work

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• On tensor spaces for rook monoid algebras
• Motzkin monoids and partial Brauer monoids
• Diagram monoids and Graham-Houghton graphs: idempotents and generating sets of ideals
• Partition algebras.
• Relations between Young's natural and the Kazhdan-Lusztig representations of \(S_ n\)
• On central idempotents in the partition algebra
• Representations of the \(q\)-rook monoid.
• Presentations for rook partition monoids and algebras and their singular ideals
• The efficient computation of Fourier transforms on semisimple algebras
• Representations of the rook monoid.
• The structure of the partition algebras
• Set-partition tableaux and representations of diagram algebras
• Lectures in algebraic combinatorics. Young's construction, seminormal representations, \(\mathfrak{sl}(2)\) representations, heaps, basics on finite fields
• An insertion algorithm on multiset partitions with applications to diagram algebras
• Partition algebras and the invariant theory of the symmetric group
• Partition algebras Pk(n) with 2k>n and the fundamental theorems of invariant theory for the symmetric group Sn
• TEMPERLEY-LIEB ALGEBRAS FOR NON-PLANAR STATISTICAL MECHANICS — THE PARTITION ALGEBRA CONSTRUCTION
• The partition algebra and the Potts model transfer matrix spectrum in high dimensions
• Twisted Brauer monoids
• Representations of the Rook-Brauer Algebra
• A Specht module analog for the rook monoid