  We investigate the partially asymmetric exclusion process (PASEP) with open
boundaries when the reverse hopping rate of particles q=-1, using a
representation of the PASEP algebra related to the al-Salam Chihara
polynomials. When q=-1 the representation is two-dimensional, which allows for
straightforward calculation of the normalization, current and density. We note
that these quantities behave in an a priori reasonable manner in spite of the
apparently unphysical value of q as the input, alpha, and output, beta, rates
are varied over the physical range of 0 to 1.
  As is well known, another two dimensional representation exists when 0<q<1
and abq=1, where a=(1-q)/beta -1 and b=(1-q)/beta-1, and we compare the
behaviour at q=-1 with this. An extension to generalized boundary conditions
where particles may enter and exit at both ends is briefly outlined. We also
note that a different representation related to the q-harmonic oscillator does
not admit a straightforward truncation when q=-1 and discuss why this is the
case from the perspective of a lattice path interpretation of the PASEP
normalization.
