I am interested in the detailed computation of the generalized Springer theory for spin groups (type B or D). The last sentense in Section 14 of Lusztig's *Intersection cohomology complex on a reductive group* he wrote *"It is likely that, if $(C,\mathcal{E})\in\mathcal{N}_{\chi}^{(0)}$ and $g\in C$, then the sizes of the Jordan cells $\beta(g)\in SO(V)$ give the partition $N=1+5+9+13+...$ or $N=3+7+11+15+...$."*

In other words, the sizes of Jordan blocks of the unipotent orbits that support those new cuspidal local systems that live in $Spin_N$ but not $SO_N$ were predicted as above. Has this computation been completed somewhere? And if so what are the local systems attached to these orbits? Thanks!