Equivariant vector bundles on toric varieties

Let $X$ be a toric variety, i.e. $X$ is a normal algebraic variety that admits a torus action with an open orbit. A vector bundle $E$ over $X$ is called toric if it is equivariant with respect to the torus action. We will prove that the category of toric bundles on $X$ is equivalent to the category of vector spaces with a family of decreasing $\mathbb{Z}$-filtrations that are explicitly constructed from the fan of $X$.
The talk is based on the paper (A.Klyachko, "Equivariant bundles on toral varieties", Mathematics of the USSR-Izvestiya, 1990, 35:2, 337-375).