Distance-regular graphs and the $q$-tetrahedron algebra
| dc.creator | Ito, Tatsuro | |
| dc.creator | Terwilliger, Paul | |
| dc.date | 2006-08-28 | |
| dc.date.accessioned | 2026-07-07T07:22:15Z | |
| dc.date.available | 2026-07-07T07:22:15Z | |
| dc.description | Let $Γ$ denote a distance-regular graph with classical parameters $(D,b,α,β)$ and $b\not=1$, $α=b-1$. The condition on $α$ implies that $Γ$ is formally self-dual. For $b=q^2$ we use the adjacency matrix and dual adjacency matrix to obtain an action of the $q$-tetrahedron algebra $\boxtimes_q$ on the standard module of $Γ$. We describe four algebra homomorphisms into $\boxtimes_q$ from the quantum affine algebra $U_q({\hat{\mathfrak{sl}}_2})$; using these we pull back the above $\boxtimes_q$-action to obtain four actions of $U_q({\hat{\mathfrak{sl}}_2})$ on the standard module of $Γ$. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/math/0608694 | |
| dc.identifier | http://arxiv.org/abs/math/0608694 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115591 | |
| dc.subject | Combinatorics | |
| dc.subject | Quantum Algebra | |
| dc.subject | 05E30 | |
| dc.title | Distance-regular graphs and the $q$-tetrahedron algebra | |
| dc.type | text |