Let $G$ be a reductive algebraic group and $B$ a Borel subgroup of $G$. Let $T$ be a maximal torus of $G$ contained in $B$. The $B=UT=TU$ for some unipotent subgroup $U$ of $G$. We have Bruhat decomposition $G = \cup_{w \in W} BwB = \cup_{w \in W} BwU$. Let $U$ act on $G$ by right multiplication. Then we have an embedding $B \hookrightarrow G/U$. Therefore there is an embedding $ℂ[G/U]↪ℂ[B]$.

My question is: how to write the map $ℂ[G/U]↪ℂ[B]$ explicitly? For example, let $G=GL_2$, $B$ the subgroup of all upper triangular matrices, and $U$ the subgroup consisting of all upper triangular matrices. Then we have $$ ℂ[G/U]=ℂ[g_{11},g_{21},g_{11}g_{22}−g_{12}g_{21}]$$ and $$ℂ[B]=ℂ[b_{11},b_{12},b_{22}].$$ What are the images of $g_{11},g_{21},g_{11}g_{22}−g_{12}g_{21}$? Thank you very much.