3 problems

Let $B_\natural$ be the limiting crystal obtained from the crystals $B_l$, and let $g_l:B_l\to B_\natural$ be its set-theoretic embedding. For fixed $u\in B_\natural$ and…

Let $N \in {\mathbb Z}_{\ge 2}$. Fix positive integers $k_1,\ldots,k_N$ with $k_1>\cdots>k_N$, and elements $b_i \in B_{k_i}$ for $i=1,\ldots,N$ in the…

The normal-ordering conjecture. The result of normal ordering always satisfies