  In this work we investigate the environmental dependence of the intrinsic
ellipticity correlations in cosmic shear surveys. We use the quadratic and
linear alignment model to describe the contributions by spiral and elliptical
galaxies, respectively. The density field is in both cases described by a
Gaussian random field and ellipticity correlation functions that are
conditional on the environment of the galaxies are constructed by sampling
random values for the tidal tensor and inertial tensor. The covariance of the
Gaussian random process from which the tensor entries are drawn is decomposed
by means of a spherical Fourier-Bessel transformation of the density field. The
dependence on environment is modelled by the number of positive eigenvalues of
the tidal tensor, which allows a differentiation between voids, sheets,
filaments and superclusters. We find that elliptical galaxies align strongest
in elongated structures such as sheets and filaments with an amplitude almost
an order of magnitude higher compared to the alignment in clusters or voids. In
contrast to this, spiral galaxies align equally strong in all environments.
Cross-alignments between different environments are smaller than the respective
auto-correlations subject to the Cauchy-Schwarz inequality which is an
effective bound on their amplitude. Furthermore, we find misalignment between
inertial and tidal tensor to be stronger in anisotropic regions compared to
clusters or voids. While the imprint of weak lensing on galaxy ellipticities is
agnostic about the environment, using environment information can help to
distinguish between lensing and the intrinsic alignment signal.
