Abstract
We study relations between quantum sl( n) and quantum sl( k) when q n+ k = ±1. We show that after restriction to type II representations, the commutant of U q sl( n) in Y nk ⊗ L and the commutant of U q sl(k) in 1Y kn ⊗L (where Y is a young tableau and 1 Y its transpose with respect to NW-SE diagonal) are mapped onto each other by R nk → R kn −1. Applications to lattice integrable models and link polynomials are discussed. We show in particular that the link polynomials built from U q sl(n), Y and U q sl(k), 1Y take complex conjugate values when q n + k = ± 1.
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