5 problems

Cube conjecture. The cell-decomposed space $Y_{ge 0}$ is homeomorphic to an $(n-1)$-dimensional cube.

Integrality conjecture. In this basis, non-integral structure constants occur only in Lie types $D$ and $E$.

Let $n$ be a positive integer with $n\geq 2$, let $Y$ be the Peterson variety in the complete flag variety of $\mathbb C^n$, and let the circle group $\mathbb S^1$ act on $Y$ as sp…

Let $G$ be a classical Lie group, let $\mathfrak P$ be the Peterson Hessenberg space, and write the push-forward of a Peterson-Schubert class as … where $a_{v_J}$ is the coefficien…

Let ${\rm Pet}_n$ be the Peterson variety, let $gB\in {\rm Pet}_n$, and let ${\mathfrak m}_{gB}$ be the maximal ideal of the local ring ${\mathcal O}_{gB,{\rm Pet}_n}$. Write…