The Terwilliger algebra of a distance-regular graph that supports a spin model

DOI10.1007/s10801-005-6913-1zbMath1064.05152OpenAlexW2005902176MaRDI QIDQ1781821

Nadine Wolff, John S. IV. Caughman

Publication date: 8 June 2005

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10801-005-6913-1

zbMATH Keywords

irreducible \(T\)-modules

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30)

Related Items

Spin Leonard pairs ⋮ Compatibility and companions for Leonard pairs ⋮ On the Terwilliger algebra of distance-biregular graphs ⋮ On standard bases of irreducible modules of Terwilliger algebras of Doob schemes ⋮ Near-bipartite Leonard pairs ⋮ On symmetric association schemes and associated quotient-polynomial graphs ⋮ Sharp tridiagonal pairs ⋮ Towards a classification of the tridiagonal pairs ⋮ Leonard triples of \(q\)-Racah type and their pseudo intertwiners ⋮ The structure of a tridiagonal pair ⋮ The subconstituent algebra of a bipartite distance-regular graph; thin modules with endpoint two ⋮ The quantum adjacency algebra and subconstituent algebra of a graph ⋮ Leonard pairs, spin models, and distance-regular graphs ⋮ Tridiagonal pairs of \(q\)-Racah-type and the \(q\)-tetrahedron algebra ⋮ On bipartite graphs with exactly one irreducible \(T\)-module with endpoint 1, which is thin ⋮ A diagram associated with the subconstituent algebra of a distance-regular graph ⋮ Commutative association schemes ⋮ Certain graphs with exactly one irreducible \(T\)-module with endpoint 1, which is thin

Cites Work

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• The irreducible modules of the Terwilliger algebras of Doob schemes
• The subconstituent algebra of an association scheme. I
• Characterization of H(n,q) by the parameters
• Bose-Mesner algebras related to type II matrices and spin models
• Distance-regular graphs which support a spin model are thin
• The Terwilliger algebras of bipartite \(P\)- and \(Q\)-polynomial schemes
• Some formulas for spin models on distance-regular graphs
• 2-homogeneous bipartite distance-regular graphs
• Bipartite distance-regular graphs with an eigenvalue of multiplicity \(k\)
• Generalized generalized spin models (four-weight spin models)
• CLASSIFICATION OF SMALL SPIN MODELS
• Spin models and strongly hyper-self-dual Bose-Mesner algebras

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