The Terwilliger algebra of a 2-homogeneous bipartite distance-regular graph

DOI10.1006/jctb.2000.2002zbMath1023.05139OpenAlexW1965662251MaRDI QIDQ1850514

Curtin, Brian

Publication date: 10 December 2002

Published in: Journal of Combinatorial Theory. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jctb.2000.2002

zbMATH Keywords

quantum universal enveloping algebra

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30) Distance in graphs (05C12)

Related Items (18)

Normalized Leonard pairs and Askey--Wilson relations ⋮ Homogeneity of a distance-regular graph which supports a spin model ⋮ Bipartite \(Q\)-polynomial distance-regular graphs and uniform posets ⋮ The Terwilliger algebra of the incidence graphs of Johnson geometry ⋮ \(Q\)-polynomial distance-regular graphs and a double affine Hecke algebra of rank one ⋮ The Terwilliger algebras of Johnson graphs ⋮ Distance-regular graphs of \(q\)-Racah type and the universal Askey-Wilson algebra ⋮ The local eigenvalues of a bipartite distance-regular graph ⋮ Askey-Wilson relations and Leonard pairs ⋮ The subconstituent algebra of a bipartite distance-regular graph; thin modules with endpoint two ⋮ Spin models and strongly hyper-self-dual Bose-Mesner algebras ⋮ The Terwilliger algebras of Grassmann graphs ⋮ 1-homogeneous, pseudo-1-homogeneous, and 1-thin distance-regular graphs ⋮ The Terwilliger algebra of an almost-bipartite \(P\)- and \(Q\)-polynomial association scheme ⋮ Structure of thin irreducible modules of a \(Q\)-polynomial distance-regular graph ⋮ The Terwilliger algebra of the incidence graphs of Johnson geometry. II. ⋮ A diagram associated with the subconstituent algebra of a distance-regular graph ⋮ Almost 2-homogeneous bipartite distance-regular graphs

Cites Work

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• The subconstituent algebra of an association scheme. I
• The Terwilliger algebra of the hypercube
• Parameters of association schemes that are both P- and Q-polynomial
• Balanced sets and Q-polynomial association schemes
• 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
• Spin models on bipartite distance-regular graphs
• Bipartite distance-regular graphs with an eigenvalue of multiplicity \(k\)
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• A Set of Orthogonal Polynomials That Generalize the Racah Coefficients or $6 - j$ Symbols
• Orthogonal Polynomials, Duality and Association Schemes
• Distance-regular graphs related to the quantum enveloping algebra of \(sl(2)\)

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