Title: Galaxy properties from the outskirts to the core of a protocluster at z=3.699

Abstract: We present follow-up spectroscopy on a protocluster candidate selected from the wide-field imaging of the Hyper SuprimeCam Subaru Strategic Programme. The target protocluster candidate was identified as a $4.5\sigma$ overdense region of $g$-dropout galaxies, and the redshifts of $g$-dropout galaxies are determined by detecting their Ly$\alpha$ emission. Thirteen galaxies, at least, are found to be clustering in the narrow redshift range of $\Delta z<0.05$ at $z=3.699$. This is clear evidence of the presence of a protocluster in the target region. Following the discovery of the protocluster at $z=3.699$, the physical properties and three-dimensional distribution of its member galaxies are investigated. Based on spectroscopically-confirmed $g$-dropout galaxies, we find an overabundance of rest-frame ultraviolet (UV) bright galaxies in the protocluster. The UV brightest protocluster member turns out to be an active galactic nucleus, and the other UV brighter members tend to show smaller Ly$\alpha$ equivalent widths than field counterparts. The member galaxies tend to densely populate near the centre of the protocluster, but the separation from the nearest neighbour rather than the distance from the centre of the protocluster is more tightly correlated to galaxy properties, implying that the protocluster is still in an early phase of cluster formation and only close neighbours have a significant impact on the physical properties of protocluster members. The number density of massive galaxies, selected from an archival photometric-redshift catalogue, is higher near the centre of the protocluster, while dusty starburst galaxies are distributed on the outskirts. These observational results suggest that the protocluster consists of multiple galaxy populations, whose spatial distributions may hint at the developmental phase of the galaxy cluster.