SH$^c$ Realization of Minimal Model CFT: Triality, Poset and Burge Condition

Understand

Recently an orthogonal basis of $\mathcal{W}_N$-algebra (AFLT basis) labeled by $N$-tuple Young diagrams was found in the context of 4D/2D duality.

• Recursion relations among the basis are summarized in the form of an algebra SH$^c$ which is universal for any $N$.
• We show that it has an $\mathfrak{S}_3$ automorphism which is referred to as triality.
• We study the level-rank duality between minimal models, which is a special example of the automorphism.