Generators of a Bosonic VOA and Connections to a Boundary VOA

We show how to identify generators of bosonic VOAs associated with $T_{[n-1,1]}^{[1^n]}(SU(n))$ and $T_{[n-1,1^2]}^{[2,1^{n-1}]}(SU(n+1))$, and conjecture that the algebraic structure of these VOAs can be constructed by these generators. We also find out that the boundary VOA associated with $T_{[n-1,1]}^{[1^n]}(SU(n))$ naturally includes the bosonic VOA.