TY - JOUR

T1 - The terwilliger algebra of the twisted grassmann graph

T2 - The thin case

AU - Tanaka, Hajime

AU - Wang, Tao

N1 - Publisher Copyright:
© The authors.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

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U2 - 10.37236/9873

DO - 10.37236/9873

M3 - Article

AN - SCOPUS:85095448716

SN - 1077-8926

VL - 27

SP - 1

EP - 22

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

IS - 4

M1 - P4.15

ER -