Cellular Algebra of $A_2$ webs

Azat M. Gainutdinov, Jesper Lykke Jacobsen, Yueheng Li

We introduce a diagram algebra ${\mathcal{K}}_L$ based on Kuperberg's $A_2$-webs and prove a Schur--Weyl duality $\mathcal{K}_L \cong \operatorname{End}_{U_q(\mathfrak{sl}_3)}((V^+ \…