Stable sl_N homology is generated by the x_k and μ_k

For the Koszul model of stable $\operatorname{sl}_N$-homology, let $x_k$ be the even generators and let $mu_k$ be the cycles defined from the generating functions $x(\tau)$ and $\xi(\tau)$ by

$$\mu(\tau)=\sum_{k=1}^{\infty}\mu_k\tau^{k-1}=N\dot{x}(\tau)\xi(\tau)-x(\tau)\dot{\xi}(\tau).$$

The generation conjecture. The homology of $d_N$ is generated as an algebra by $x_k$ and $mu_k$. This gives a proposed algebraic description of stable $\operatorname{sl}_N$-homology; the source provides no resolution status beyond stating the conjecture.