The Clebsch-Gordan coefficients of \(U(\mathfrak{sl}_2)\) and the Terwilliger algebras of Johnson graphs

DOI10.1016/j.jcta.2023.105833zbMath1530.05198arXiv2212.05385OpenAlexW4388718360MaRDI QIDQ6187333

Hau-Wen Huang

Publication date: 15 January 2024

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

Full work available at URL: https://arxiv.org/abs/2212.05385

zbMATH Keywords

Clebsch-Gordan coefficientsJohnson graphsHahn polynomialsTerwilliger algebras

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30) Representations of orders, lattices, algebras over commutative rings (16G30)

Cites Work

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• The subconstituent algebra of an association scheme. I
• The subconstituent algebra of an association scheme. III
• The subconstituent algebra of an association scheme. II
• The Terwilliger algebra of the hypercube
• Finite-dimensional irreducible modules of the universal Askey-Wilson algebra
• Normalized Leonard pairs and Askey--Wilson relations
• The Terwilliger algebra of the Johnson schemes
• An algebra associated with a subspace lattice over a finite field and its relation to the quantum affine algebra \(U_q(\hat{\mathfrak{sl}}_2)\)
• An algebra behind the Clebsch-Gordan coefficients of \(U_q(\mathfrak{sl}_2)\)
• Finite-dimensional irreducible modules of the Racah algebra at characteristic zero
• Finite-dimensional irreducible modules of the Bannai-Ito algebra at characteristic zero
• The Terwilliger algebra of the Grassmann scheme \(J_q(N,D)\) revisited from the viewpoint of the quantum affine algebra \(U_q(\hat{\mathfrak{sl}}_2)\)
• The Terwilliger algebra of the Johnson scheme \(J(N, D)\) revisited from the viewpoint of group representations
• An observation on Leonard system parameters for the Terwilliger algebra of the Johnson scheme \(J(N, D)\)
• More on the Terwilliger algebra of Johnson schemes
• A connection behind the Terwilliger algebras of \(H(D,2)\) and \(\frac{ 1}{ 2} H(D,2)\)
• Entanglement of free fermions on Johnson graphs

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