Abstract
Theq=0 combinatorics for\(U_q (\widehat{\mathfrak{s}\mathfrak{l}}(n))\) is studied in connection with solvable lattice models. Crystal bases of highest weight representations of\(U_q (\widehat{\mathfrak{s}\mathfrak{l}}(n))\) are labelled by paths which were introduced as labels of corner transfer matrix eigenvectors atq=0. It is shown that the crystal graphs for finite tensor products ofl-th symmetric tensor representations of\(U_q (\widehat{\mathfrak{s}\mathfrak{l}}(n))\) approximate the crystal graphs of levell representations of\(U_q (\widehat{\mathfrak{s}\mathfrak{l}}(n))\). The identification is made between restricted paths for the RSOS models and highest weight vectors in the crystal graphs of tensor modules for\(U_q (\widehat{\mathfrak{s}\mathfrak{l}}(n))\).
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Communicated by N. Yu. Reshetikhin
Partially supported by NSF grant MDA904-90-H-4039
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Jimbo, M., Misra, K.C., Miwa, T. et al. Combinatorics of representations of\(U_q (\widehat{\mathfrak{s}\mathfrak{l}}(n))\) atq=0. Commun.Math. Phys. 136, 543–566 (1991). https://doi.org/10.1007/BF02099073
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DOI: https://doi.org/10.1007/BF02099073