  A small cluster of massive stars residing in the Galactic center,
collectively known as IRS13E, is of special interest due to its close proximity
to Sgr A* and the possibility that an embedded intermediate-mass black hole
(IMBH) binds its member stars. It has been suggested that colliding winds from
two member stars, both classified as Wolf-Rayet type, are responsible for the
observed X-ray, infrared and radio emission from IRS13E. We have conducted an
in-depth study of the X-ray spatial, temporal and spectral properties of
IRS13E, based on 5.6 Ms of ultra-deep Chandra observations obtained over 20
years. These X-ray observations show no significant evidence for source
variability. We have also explored the kinematics of the cluster members, using
Keck near-infrared imaging and spectroscopic data on a 14-yr baseline that
considerably improve the accuracy of stars' proper motions. The observations
are interpreted using 3-dimensional hydrodynamical simulations of colliding
winds tailored to match the physical conditions of IRS13E, leading us to
conclude that the observed X-ray spectrum and morphology can be well explained
by the colliding wind scenario, in the meantime offering no support for the
presence of a putative IMBH. An IMBH more massive than a few
$10^3{\rm~M_\odot}$ is also strongly disfavored by the stellar kinematics.
