The Haglund–Haiman–Loehr–Remmel–Ulyanov conjecture for diagonal coinvariants

Let $DR_n$ be the diagonal coinvariant ring with its ${\mathfrak{S}}_n$-action and bigrading, and let ${\mathcal{F}}(DR_n,z;q,t)$ denote its bigraded Frobenius series. For each partition $\lambda\subset\delta_n=(n-1,n-2,\ldots,1,0)$, define

$$D_n^\lambda(z;q)=\sum_{T\in {\mathrm{SSYT}}(\lambda +(1^n)/\lambda)}q^{{\mathrm{dinv}}(T)}z^T,$$

and set

$$D_n(z;q,t)=\sum_{\lambda\subset\delta_n}t^{|\delta_n/\lambda|}D_n^\lambda(z;q).$$

Haglund–Haiman–Loehr–Remmel–Ulyanov conjecture. We have an identity

$${\mathcal{F}}(DR_n,z;q,t)=D_n(z;q,t).$$

This conjecture gives a combinatorial formula for the monomial symmetric function expansion of the Frobenius series of diagonal coinvariants. It was proposed by Haglund, Haiman, Loehr, Remmel, and Ulyanov; the supplied source does not state whether it has been resolved.