Universal Verma Modules and the Misra-Miwa Fock Space

Figure 2

The partition enclosed by the thick lines is 𝜆=(10,10,8,8,8,6,6,6,6,1,1). If 𝑘=6 then 𝐴(𝜆,<6)={𝑎₁,𝑎₃}, 𝑅(𝜆,<6)={𝑔₂,𝑔₅}, andev_𝜆(𝑠₆)=([2]/[3])([3]/[4])([4]/[5])([7]/[8])([8]/[9])=([2]/[5])([7]/[9])=([𝑐(𝑔₅)−𝑐(𝑏)][𝑐(𝑔₂)−𝑐(𝑏)])/([𝑐(𝑎₃)−𝑐(𝑏)][𝑐(𝑎₁)−𝑐(𝑏)]). The factors in the numerator of the first expression are displayed. These are the 𝑞-integers corresponding to the hook lengths of the boxes in the same column as the addable box 𝑏 in row 6.