3 problems

Parabolic Temperley–Lieb relations conjecture. These functors should satisfy the natural isomorphisms corresponding to the defining relations of the Temperley–Lieb category, with…

For integers $n$ and $k$, let $D^b(\mathcal O_{k,n-k})$ be the bounded derived category of the relevant parabolic category, and define functors … … by…

Let $F^{n}_{A_{2n-1}}$ be the relevant Fock space, and let $v_c$ denote the graded vector associated with a crossingless matching $c$. Temperley–Lieb representation conjecture. The…