Johnson graphs as slices of a hypercube and an algebra homomorphism from the universal Racah algebra into $U({\mathfrak{sl}}_2)$

Hau-Wen Huang, Chia-Yi Wen

From the viewpoint of Johnson graphs as slices of a hypercube, we derive a novel algebra homomorphism $♯$ from the universal Racah algebra $\Re$ into $U({\mathfrak{sl}}_2)$. We…