  The exact parity model (EPM) is a simple extension of the Standard Model
which reinstates parity invariance as an unbroken symmetry of nature. The
mirror matter sector of the model can interact with ordinary matter through
gauge boson mixing, Higgs boson mixing and, if neutrinos are massive, through
neutrino mixing. The last effect has experimental support through the observed
solar and atmospheric neutrino anomalies. In this paper we show that the exact
parity model can be formulated in a quaternionic framework. This suggests that
the idea of mirror matter and exact parity may have profound implications for
the mathematical formulation of quantum theory.
