A distance-regular graph Γ affords a spin model if and only if each irreducible module for every Terwilliger algebra of Γ takes the form described by Caughman et al., with explicit construction given for q-Racah type.
Caughman IV, N.Wolff, The Terwilliger algebra of a distance-reg ular graph that supports a spin model, J
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Leonard pairs, spin models, and distance-regular graphs
A distance-regular graph Γ affords a spin model if and only if each irreducible module for every Terwilliger algebra of Γ takes the form described by Caughman et al., with explicit construction given for q-Racah type.