  Given any finite quiver, we consider a complete flag of vector spaces over
each vertex. Consider the unipotent invariant subalgebra of the coordinate ring
of the filtered quiver representation subspace. We prove that the dimension of
the algebraic variety of the unipotent invariant subalgebra is finite. We also
construct an ADHM analog for the Borel subalgebra setting, showing its
birationality to the isospectral Hilbert scheme. Quiver-graded Steinberg
varieties, quantum Hamiltonian reduction, and deformation quantization
constructions for the nonreductive setting are discussed, ending with open
problems.
