BPS States, Crystals, and Matrices

Figure 12

(a): toric diagram for the conifold and arrow representation of 𝐴₊ and 𝑊₁. (b): for chambers with negative 𝑅 and positive 𝑛−1<𝐵<𝑛 the crystals are given by finite pyramid partitions with 𝑛−1 additional corners, represented by 𝑛−1 stones in the top row (the figure shows the case 𝑛=4). The generating function is given by 𝑍_𝑛|1=⟨0|(𝑊₁)^𝑛|0⟩ which reproduces the result (2.27).

(a)

(b)