  Addressing how strong UV radiation affects galaxy formation is central to
understanding their evolution. The quenching of star formation via strong UV
radiation (from starbursts or AGN) has been proposed in various scenes to solve
certain astrophysical problems. Around luminous sources, some evidence of
decreased star formation has been found but is limited to a handful of
individual cases. No direct, conclusive evidence on the actual role of strong
UV radiation in quenching star formation has been found. Here we present
statistical evidence of decreased number density of faint (AB magnitude $\geq$
24.75 mag) Ly\alpha emitters (LAEs) around bright (AB magnitude < 24.75 mag)
LAEs even when the radius goes up to 10 pMpc for $z$ $\simeq$ 5.7 LAEs. A
similar trend is found for z $\simeq$ 6.6 LAEs but only within 1 pMpc radius
from the bright LAEs. We use a large sample of 1077 (962) LAEs at $z$ $\simeq$
5.7 ($z$ $\simeq$ 6.6) selected in total areas of 14 (21) deg$^2$ with
Subaru/Hyper Suprime-Cam narrow-band data, and thus, the result is of
statistical significance for the first time at these high redshift ranges. A
simple analytical calculation indicates that the radiation from the central LAE
is not enough to suppress LAEs with AB mag $\geq$ 24.75 mag around them,
suggesting additional physical mechanisms we are unaware of are at work. Our
results clearly show that the environment is at work for the galaxy formation
at $z$ $\sim$ 6 in the Universe.
