Fomin–Kirillov's infinite-dimensionality conjecture

Let $\EuScript{E}_m$ be the Fomin–Kirillov algebra over a field $\mathbf{k}$ associated with the symmetric group $\mathbb{S}_m$. Fomin–Kirillov's conjecture. The algebra $\EuScript{E}_m$ is infinite dimensional for all $m\geq 6$. This conjecture asks for the dimension of the Fomin–Kirillov algebra; it is known that $\EuScript{E}_m$ is finite dimensional for all $m\leq 5$, while the asserted infinite dimensionality for $m\geq 6$ remains open.