  We investigate spatial correlations of strain fluctuations in sheared
colloidal glasses and simulations of sheared amorphous solids. The correlations
reveal a quadrupolar symmetry reminiscent of the strain field due to an
Eshelby's inclusion. However, they display an algebraic decay $1/r^{\alpha}$,
where the exponent $\alpha$ is close to $1$ in the steady state, unlike the
Eshelby field, for which $\alpha=3$ . The exponent takes values between $3$ to
$1$ in the transient stages of deformation. We explain these observations using
a simple model based on interacting Eshelby inclusions. As the system is
sheared beyond the linear response to plastic flow, the density correlations of
inclusions are enhanced and it emerges as key to understanding the
elastoplastic response of the system to applied shear.
