The t=-1 phenomenon for M-polynomials of graded Lie algebra components

Let $\Delta(1)$ be the weight poset associated with a $\mathbb Z$-grading, let $\EuScript M_{\Delta(1)}(t)$ be its M-polynomial, and define the dual ideal of an upper ideal $I$ by

$$I^*=\Delta(1)\setminus w_0(I),$$

where $w_0$ is the longest element of the degree-zero Weyl group.

The t=-1 phenomenon conjecture. The value $\EuScript M_{\Delta(1)}(-1)$ equals the number of upper ideals $I$ satisfying $I^*=I$.

The assertion is known in the abelian and extra-special cases, while a conceptual proof in general remains open.