  We search $t$-matrix poles for $\Lambda N-\Sigma N$ coupling interactions
using two soft core models of the Nijmegen group which bind the hypertriton at
the correct binding energy, and hard core models which are still influential in
hypernuclear physics. To treat the hard core potentials, a useful method for
calculating the off-shell $t$-matrix is proposed. We find poles close to the
$\Sigma N$ threshold in the second or third quadrant of the complex plane of
the $\Sigma N$ relative momentum. The relation between the poles and the shape
of the $\Lambda N$ elastic total cross section is discussed based on a
so-called uniformization by which two-channel $t$-matrices become single-valued
on a complex valuable. We also find poles near the $\Lambda N$ threshold. These
are correlated to the $S$-wave $\Lambda N$ scattering lengths, the values of
which have yet to be determined.
