  Let $G$ be a semisimple simply connected complex algebraic group. Let $U$ be
the unipotent radical of a Borel subgroup in $G$. We describe the coordinate
rings of $U$ (resp., $G/U$, $G$) in terms of two (resp., four, eight)
birational charts introduced in [L94, L19] in connection with the study of
total positivity.
