Infinite-dimensionality conjecture for the Nichols–Woronowicz algebra of the symmetric group

Let $\mathbb{S}_m$ be the symmetric group, and let $\EuScript{B}_{\mathbb{S}_m}$ be its Nichols–Woronowicz algebra model for Schubert calculus. Infinite-dimensionality conjecture. The algebra $\EuScript{B}_{\mathbb{S}_m}$ is infinite dimensional for all $m\geq 6$. The algebra $\EuScript{B}_{\mathbb{S}_m}$ is known to be a quotient of the Fomin–Kirillov algebra $\EuScript{E}_m$, and it is conjecturally isomorphic to it; proving this infinite-dimensionality statement would therefore suffice to prove the Fomin–Kirillov conjecture.