I am looking for presentations of partial or complete flag varieties as GIT quotients of affine ~~varieties~~ spaces. That is, for a choice of of dimensions $0=d_1<d_2<\dots<d_k = n$, I would like to find examples of an affine ~~variety~~ space $V/\mathbb{C}$, a reductive group G acting on V, and a linearization $L$ such that the GIT quotient $V//G$ is equal to the flag variety $Fl(d_1,d_2,\dots,d_k)$.

Of course $\mathbb{P}^{n-1}$ is an easy example for $Fl(1,n)$, where $V = \mathbb{C}^{n}$ and $G = \mathbb{C}^{\times}$. And the Grassmannian $Fl(k,n) = Gr(k, {n})$ can be constructed as a GIT quotient of the vector space $M_{k,{n}}$ of $k\times n$ matrices $Gr(k, {n}) = M_{k,{n}}//GL(k)$, where $GL(k)$ acts as matrix multiplication on the left.

Are there constructions that work for more general choices of $d_i$? Does anyone know of any other examples or have recommendations of where I might look for them?

varieties(which as Jason points out is very easy to arrange), or as quotients of affinespaces(as in your examples)? $\endgroup$ – Allen Knutson Aug 21 '13 at 13:51