On Penrose limit of elliptic branes

We discuss a Penrose limit of an elliptic brane configuration with $N_1$ NS5 and $N_2$ D4 branes. This background is T-dual to $N_1$ D3 branes at a fixed point of a $\mathbf{C}^3/\mathbf{Z}_{N_2}$ singularity and the T-duality survives the Penrose limit. The triple scaling limit of $N_1$ and $N_2$ gives rise to IIA pp-wave solution with a space-like compact direction. We identify the quiver gauge theory operators and argue that upon exchange of the momentum along the compact direction and the winding number these operators coincide with the operators derived in the dual type IIB description. We also find a new Penrose limit of the type IIB background and the corresponding limit in the type IIA picture. In the coordinate system we use there are two manifest space-like isometries. The quiver gauge theory operator duals of the string states are built of three bosonic fields.