Root of unity symmetries in the 8 and 6 vertex models

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We review the recently discovered symmetries of the 8 and 6 vertex models which exist at roots of unity and present their relation with representation theory of affine Lie algebras, Drinfeld polynomials and Bethe vectors.
13 pages, to appear in Proceedings of the RIMS 2004 workshop on "Recent Progress in Solvable Lattice Models"

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