## Abstract

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 E_{i}^{∗}(x) = diag(v_{i}) (i = 0, 1, 2, … ), where v_{i} denotes the characteristic vector of the set of vertices at distance i from x. The twisted Grassmann graph J_{q} (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 E_{i}^{∗}(x)W ≤ 1 for all i. In this paper, we determine all the irreducible T (x)-modules of J_{q} (2D + 1, D) for this “thin” case.

Original language | English |
---|---|

Article number | P4.15 |

Pages (from-to) | 1-22 |

Number of pages | 22 |

Journal | Electronic Journal of Combinatorics |

Volume | 27 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2020 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics