k-multi-layered maximizer conjecture at a root-of-unity specialization
Fix k∈Z>0k\in\mathbb{Z}_{>0}k∈Z>0, let ζ\zetaζ be a kkk-th root of unity, and let Φwk\Phi_w^kΦwk denote the principal specialization Sw(1,q,q2,…)\mathfrak{S}_w(1,q,q^2,\ldots)Sw(1,q,q2,…) at q=ζq=\zetaq=ζ. Define … and…