COMBINATORICS OF REPRESENTATIONS OF UQ[SL(N)] AT Q = 0

The q = 0 combinatorics for U(q)(sI(n)) is studied in connection with solvable lattice models. Crystal bases of highest weight representations of U(q)(sI(n)) are labelled by paths which were introduced as labels of corner transfer matrix eigenvectors at q = 0. It is shown that the crystal graphs for finite tensor products of l-th symmetric tensor representations of U(q)(sI(n)) approximate the crystal graphs of level l representations of U(q)(sI(n)). The identification is made between restricted paths for the RSOS models and highest weight vectors in the crystal graphs of tensor modules for U(q)(sI(n)).