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We explain how to construct matrix product stationary states which arecomposed of finite-dimensional matrices. Our construction explained in thisarticle was first presented in a part of [Hieida and Sasamoto:J. Phys. A: Math.Gen. 37 (2004) 9873] for general models. In this article, we give more detailson the treatment than in the above-mentioned reference, for one-dimensionalasymmetric simple exclusion process(ASEP).

A systematic way to find and construct exact finite dimensional matrix product stationary states