The Terwilliger Algebra of a Distance-Regular Graph of Negative Type
| dc.creator | Miklavic, Stefko | |
| dc.date | 2008-04-10 | |
| dc.date.accessioned | 2026-07-07T09:31:31Z | |
| dc.date.available | 2026-07-07T09:31:31Z | |
| dc.description | Let $Γ$ denote a distance-regular graph with diameter $D \ge 3$. Assume $Γ$ has classical parameters $(D,b,α,β)$ with $b < -1$. Let $X$ denote the vertex set of $Γ$ and let $A \in MX$ denote the adjacency matrix of $Γ$. Fix $x \in X$ and let $A^* \in MX$ denote the corresponding dual adjacency matrix. Let $T$ denote the subalgebra of $MX$ generated by $A, A^*$. We call $T$ the {\em Terwilliger algebra} of $Γ$ with respect to $x$. We show that up to isomorphism there exist exactly two irreducible $T$-modules with endpoint 1; their dimensions are $D$ and $2D-2$. For these $T$-modules we display a basis consisting of eigenvectors for $A^*$, and for each basis we give the action of $A$ | |
| dc.identifier | https://arxiv.org/abs/0804.1650 | |
| dc.identifier | http://arxiv.org/abs/0804.1650 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158488 | |
| dc.subject | Combinatorics | |
| dc.subject | 05E30 | |
| dc.title | The Terwilliger Algebra of a Distance-Regular Graph of Negative Type | |
| dc.type | text |