The Terwilliger algebra of the Grassmann scheme \(J_q(N,D)\) revisited from the viewpoint of the quantum affine algebra \(U_q(\hat{\mathfrak{sl}}_2)\)

DOI10.1016/j.laa.2020.03.005zbMath1435.05239OpenAlexW3009437765MaRDI QIDQ2309682

Xiaoye Liang, Yuta Watanabe, Tatsuro Ito

Publication date: 1 April 2020

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2020.03.005

zbMATH Keywords

Terwilliger algebraquantum affine algebraGrassmann schemeLeonard system

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Association schemes, strongly regular graphs (05E30) Grassmannians, Schubert varieties, flag manifolds (14M15) Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Quantum groups (quantized function algebras) and their representations (20G42)

Related Items (8)

On the trivial \(T\)-module of a graph ⋮ The Terwilliger algebra of symplectic dual polar graphs, the subspace lattices and \(U_q(\mathrm{sl}_2)\) ⋮ On standard bases of irreducible modules of Terwilliger algebras of Doob schemes ⋮ Inclusion matrices for rainbow subsets ⋮ The Clebsch-Gordan coefficients of \(U(\mathfrak{sl}_2)\) and the Terwilliger algebras of Johnson graphs ⋮ The Terwilliger algebra of the twisted Grassmann graph: the thin case ⋮ On bipartite graphs with exactly one irreducible \(T\)-module with endpoint 1, which is thin ⋮ Certain graphs with exactly one irreducible \(T\)-module with endpoint 1, which is thin

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
• An algebra associated with a subspace lattice over a finite field and its relation to the quantum affine algebra \(U_q(\hat{\mathfrak{sl}}_2)\)
• 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 \(J(N, D)\)
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other

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