# Do we have $\mathbb{C}[G/N] = \mathbb{C}[G]^N$?

Let $G=GL_n$ and $N$ its unipotent subgroup consisting of all upper unipotent triangular matrices. Do we have $\mathbb{C}[G/N] = \mathbb{C}[G]^N$? Here $\mathbb{C}[G/N]$ is the coordinate ring of $G/N$ and $\mathbb{C}[G]^N$ is the set of functions in $\mathbb{C}[G]$ which are invariant under the action of $N$, where the action of $N$ on $G$ is given by right multiplication. Thank you very much.