FINITE-DIMENSIONAL REPRESENTATIONS OF A SHOCK ALGEBRA

The algebra describing a shock measure in the asymmetric simple exclus ion model, seen from a second class particle, has finite-dimensional r epresentations if and only if the asymmetry parameter p of the model a nd the left and right asymptotic densities rho(+/-) of the shock satis fy [(1-p)/p](r)=rho(-)(1-rho(+))/rho(+)(1-rho(-)) for some integer r g reater than or equal to 1; the minimal dimension of the representation is then 2r. These representations can be used to calculate correlatio n functions in the model.