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Person re-identification (re-ID) aims at matching images of the same person across camera views. Due to varying distances between cameras and persons of interest, resolution mismatch can be expected, which would degrade re-ID performance in real-world scenarios. To overcome this problem, we propose a novel generative adversarial network to address cross-resolution person re-ID, allowing query images with varying resolutions. By advancing adversarial learning techniques, our proposed model learns resolution-invariant image representations while being able to recover the missing details in low-resolution input images. The resulting features can be jointly applied for improving re-ID performance due to preserving resolution invariance and recovering re-ID oriented discriminative details. Extensive experimental results on five standard person re-ID benchmarks confirm the effectiveness of our method and the superiority over the state-of-the-art approaches, especially when the input resolutions are not seen during training. Furthermore, the experimental results on two vehicle re-ID benchmarks also confirm the generalization of our model on cross-resolution visual tasks. The extensions of semi-supervised settings further support the use of our proposed approach to real-world scenarios and applications.