4 problems

Let $\mu^1,\mu^2,\mu^3$ be partitions, and let $W_{\mu^1,\mu^2,\mu^3}(q)$ denote the topological vertex. For $i,j\in\{1,2,3\}$ and $m,n\geq 0$, let $A_{mn}^{ij}(q)$ be the explicit…

Let the topological vertex be regarded in the fermionic picture, and let the fermionic vacuum vector belong to the $3$-component fermionic Fock space. A Bogoliubov transform is the…

Framed ADKMV conjecture. The framed topological vertex is given by

Let $V^{(a_1,a_2,a_3)}_0\in \mathcal{F}^{(0)}_1\otimes\mathcal{F}^{(0)}_2\otimes\mathcal{F}^{(0)}_3$ be the charge-zero vector corresponding under the boson–fermion correspondence…