Cluster Variables on Certain Double Bruhat Cells of Type $(u,e)$ and Monomial Realizations of Crystal Bases of Type A

Yuki Kanakubo, Toshiki Nakashima

Let $G$ be a simply connected simple algebraic group over $\mathbb{C}$, $B$ and $B_{-}$ be two opposite Borel subgroups in $G$ and $W$ be the Weyl group. For $u$, $v\in W$, it is kno…