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The Terwilliger algebra of the Johnson scheme \(J(N, D)\) revisited from the viewpoint of group representations. (English) Zbl 1415.05181

Summary: Let \(T = T(x_0)\) be the Terwilliger algebra of the Johnson scheme \(J(N, D)\), where \(x_0\) is a fixed base point. In [X. Liang et al., Graphs Comb. 33, No. 1, 149–156 (2017; Zbl 1372.05234)], an observation is made on the parameters of Leonard systems that arise from the irreducible representations of \(T\). This paper accounts for the observation from the viewpoint of group representations. In particular, it is shown that \(T\) is isomorphic to the centralizer algebra for the stabilizer of the base point \(x_0\) in the automorphism group of \(J(N, D)\).

MSC:

05E10 Combinatorial aspects of representation theory
05E30 Association schemes, strongly regular graphs
05E18 Group actions on combinatorial structures

Citations:

Zbl 1372.05234
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References:

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[3] Liang, X.; Tan, Y.-Y.; Ito, T., An observation on Leonard system parameters for the Terwilliger algebra of the Johnson scheme \(J(N, D)\), Graph Combin., 33, 149-156 (2017) · Zbl 1372.05234
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