  EX Lup is a well-studied T Tauri star that represents the prototype of young
eruptive stars EXors. In this paper we analyze new adaptive optics imaging and
spectroscopic observations of EX Lup and its circumstellar environment in
near-infrared in its quiescent phase. We observed EX Lup with the high contrast
imager SPHERE/IRDIS in the dual-beam polarimetric imaging mode to resolve the
circumstellar environment in near-infrared scattered light. We complemented
these data with earlier SINFONI spectroscopy. We resolve for the first time in
scattered light a compact feature around EX Lup azimuthally extending from
280deg to 360deg, and radially extending from 0.3arcsec to 0.55arcsec in the
plane of the disk. We explore two different scenarios for the detected
emission. One accounting for the emission as coming from the brightened walls
of the cavity excavated by the outflow whose presence was suggested by ALMA
observations in the J=3-2 line of 12CO. The other accounts for the emission as
coming from an inclined disk. We detect for the first time a more extended
circumstellar disk in scattered light, which shows that a region between 10 and
30 au is depleted of mum-size grains. We compare the J-, H- and K-band spectra
obtained with SINFONI in quiescence with the spectra taken during the outburst,
showing that all the emission lines were due to the episodic accretion event.
Conclusions. Based on the morphology analysis we favour the scenario in which
the scattered light is coming from a circumstellar disk rather than the outflow
around EX Lup. We analyze the origin of the observed feature either as coming
from a continuous circumstellar disk with a cavity, or from the illuminated
wall of the outer disk or from a shadowed disk. Moreover, we discuss what is
the origin of the mum-size grains depleted region, exploring the possibility
that a sub-stellar companion may be the cause of it.
