  In 2+1 dimensions the global U($2N$) symmetry associated with massless Dirac
fermions is broken to U($N)\otimes$U($N$) by a parity-invariant mass. I will
show how to adapt the domain wall formulation to recover the U($2N$)-invariant
limit in interacting fermion models as the domain wall separation is increased.
In particular, I will focus on the issue of potential dynamical mass generation
in the Thirring model, postulated to take place for $N$ less than some critical
$N_c$. I will present results of simulations of the model using both HMC
($N=2$) and RHMC ($N=1$) algorithms, and show that the outcome is very
different from previous numerical studies of the model made with staggered
fermions, where the corresponding pattern of symmetry breaking is distinct.
