  The equatorial symmetry of the Kerr black hole is generically broken in
models of quantum gravity. Nevertheless, most phenomenological models start
from the assumption of equatorial symmetry, and little attention has been given
to the observability of this smoking gun signature of beyond-GR physics.
Extreme mass-ratio inspirals (EMRIs), in particular, are known to sensitively
probe supermassive black holes near their horizon; yet estimates for
constraints on deviations from Kerr in space-based gravitational wave
observations (e.g. with LISA) of such systems are currently based on
equatorially symmetric models. We use modified "analytic kludge" waveforms to
estimate how accurately LISA will be able to measure or constrain equatorial
symmetry breaking, in the form of the lowest-lying odd parity multipole moments
$S_2, M_3$. We find that the dimensionless multipole ratios such as $S_2/M^3$
will typically be detectable for LISA EMRIs with a measurement accuracy of
$\Delta(S_2/M^3) \sim 1\%$; this will set a strong constraint on the breaking
of equatorial symmetry.
