Temperley–Lieb representation conjecture for graded crossingless-matching vectors

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 span of the graded vectors $v_c$ in $F^{n}_{A_{2n-1}}$ forms a Temperley–Lieb representation. This conjectural representation is intended to connect the Heisenberg-algebra Fock-space construction with braid closures and the Jones polynomial; the source does not establish the conjecture.