The six-vertex model at roots of unity and some highest weight representations of the sl2 loop algebra
نویسنده
چکیده
We discuss irreducible highest weight representations of the sl2 loop algebra and reducible indecomposable ones in association with the sl2 loop algebra symmetry of the six-vertex model at roots of unity. We formulate an elementary proof that every highest weight representation with distinct evaluation parameters is irreducible. We present a general criteria for a highest weight representation to be irreducble. We also give an example of a reducible indecomposable highest weight representation and discuss its dimensionality.
منابع مشابه
XXZ Bethe states as highest weight vectors of the sl2 loop algebra at roots of unity
We show that regular Bethe ansatz eigenvectors of the XXZ spin chain at roots of unity are highest weight vectors and generate irreducible representations of the sl2 loop algebra. We show it in some sectors with respect to eigenvalues of the total spin operator SZ . Here the parameter q, which is related to the XXZ anisotropy ∆ through ∆ = (q + q−1)/2, is given by a root of unity, q2N = 1, for ...
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