Distance-regular graphs and the q-tetrahedron algebra

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Let Γ denote a distance-regular graph with classical parameters (D,b,α,β) and b=1, α=b-1. The condition on α implies that Γ is formally self-dual. For b=q² we use the adjacency matrix and dual adjacency matrix to obtain an action of the q-tetrahedron algebra on the standard module of Γ. We describe four algebra homomorphisms into from the quantum affine algebra Uq(sl₂); using these we pull back the above -action to obtain four actions of Uq(sl₂) on the standard module of Γ.