The terwilliger algebra of the twisted grassmann graph: The thin case

Hajime Tanaka, Tao Wang

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


The Terwilliger algebra T (x) of a finite connected simple graph Γ with respect to a vertex x is the complex semisimple matrix algebra generated by the adjacency matrix A of Γ and the diagonal matrices Ei(x) = diag(vi) (i = 0, 1, 2, … ), where vi denotes the characteristic vector of the set of vertices at distance i from x. The twisted Grassmann graph Jq (2D +1, D) discovered by Van Dam and Koolen in 2005 has two orbits of the automorphism group on its vertex set, and it is known that one of the orbits has the property that T (x) is thin whenever x is chosen from it, i.e., every irreducible T (x)-module W satisfies dim Ei(x)W ≤ 1 for all i. In this paper, we determine all the irreducible T (x)-modules of Jq (2D + 1, D) for this “thin” case.

Original languageEnglish
Article numberP4.15
Pages (from-to)1-22
Number of pages22
JournalElectronic Journal of Combinatorics
Issue number4
Publication statusPublished - 2020


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