Irreducibility criterion for a finite-dimensional highest weight representation of the sl2 loop algebra and the dimensions of reducible representations
نویسنده
چکیده
We show a necessary and sufficient condition for a finite-dimensional highest weight representation of the sl2 loop algebra to be irreducible. We present an algorithm by which we can construct all possible finite-dimensional highest weight representations that have the same given highest weight. For two simple cases, we derive dimensions of all such reducible representations, explicitly. The result should be useful in analyzing the spectra of integrable lattice models related to roots of unity representations of quantum groups, in particular, the spectral degeneracy of the XXZ spin chain at roots of unity associated with the sl2 loop algebra.
منابع مشابه
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