Cluster monomials in $\mathbb{C}[G{L}_n/N]$, a simplicial fan in the cone of semi-standard Young tableaux, and the Lusztig basis

Gleb Koshevoy

We study the cluster monomials and cluster complex in $\mathbb{C}[G{L}_n/N]$. For we consider the {\em tableau basis} in $\mathbb{C}[G{L}_n/N]$. Namely, an element ${\Delta }_T$ of the tableau b…