Algebras in higher-dimensional statistical mechanics -- the exceptional partition (mean field) algebras

DOI10.1007/BF00805850zbMath0799.16004arXivhep-th/9302095WikidataQ61847560 ScholiaQ61847560MaRDI QIDQ1318311

Hubert Saleur, Paul P. Martin

Publication date: 23 November 1994

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9302095

zbMATH Keywords

irreducible representationPotts modeltransfer matricespartition algebragenerically simple modules

Mathematics Subject Classification ID

Applications of Lie (super)algebras to physics, etc. (17B81) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60)

Related Items (19)

Tensor envelopes of regular categories ⋮ Traces on diagram algebras. II: Centralizer algebras of easy groups and new variations of the Young graph ⋮ On central idempotents in the Brauer algebra ⋮ Combinatorial Gelfand models for semisimple diagram algebras. ⋮ Representation stability for diagram algebras ⋮ On the modular representation theory of the partition algebra ⋮ The multiset partition algebra ⋮ Tonal partition algebras: fundamental and geometrical aspects of representation theory ⋮ Character orthogonality for the partition algebra and fixed points of permutations ⋮ On the decomposition matrix of the partition algebra in positive characteristic. ⋮ On representation theory of partition algebras for complex reflection groups ⋮ Set-partition tableaux and representations of diagram algebras ⋮ Gelfand models for diagram algebras ⋮ Dimensions of irreducible modules for partition algebras and tensor power multiplicities for symmetric and alternating groups ⋮ Partition algebras. ⋮ The partition algebras and a new deformation of the Schur algebras ⋮ Set-partition tableaux, symmetric group multiplicities, and partition algebra modules ⋮ On central idempotents in the partition algebra ⋮ The rook partition algebra

Cites Work

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• Zeroes of chromatic polynomials: A new approach to Beraha conjecture using quantum groups
• Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities
• On an algebraic approach to higher dimensional statistical mechanics
• Index for subfactors
• Representations of graph Temperley-Lieb algebras

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