2 problems

For each $n\geq 2$, let $P_n$ be the categorified Jones–Wenzl projector and let $U_n\colon \mathrm{q}^{2n}\Sigma^{2n-2}P_n\to P_n$ be Hogancamp's chain map. For each power $U_n^k$,…

Let $(W,S)$ be a two-colored realization over a field $\Bbbk$, with colors $s$ and $t$, and let $JW_{n_s}$ and $JW_{n_t}$ denote the corresponding Jones-Wenzl projectors. Write…