We present the results of a large-scale proper motion study of the central ~36x16 of the Milky Way, based on our high angular resolution GALACTICNUCLEUS survey (epoch 2015) combined with the HST Paschen-alpha survey (epoch 2008). Our catalogue contains roughly 80,000 stars, an unprecedented kinematic data set for this region. We describe the data analysis and the preparation of the proper motion catalogue. We verify the catalogue by comparing our results with measurements from previous work and data. We provide a preliminary analysis of the kinematics of the studied region. Foreground stars in the Galactic Disc can be easily identified via their small reddening. Consistent with previous work and with our expectations, we find that stars in the nuclear stellar disc have a smaller velocity dispersion than Bulge stars, in particular in the direction perpendicular to the Galactic Plane. The rotation of the nuclear stellar disc can be clearly seen in the proper motions parallel to the Galactic Plane. Stars on the near side of the nuclear stellar disc are less reddened than stars on its far side. Proper motions enable us to detect co-moving groups of stars that may be associated with young clusters dissolving in the Galactic Centre that are difficult to detect by other means. We demonstrate a technique based on a density clustering algorithm that can be used to find such groups of stars.
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