The six-vertex model at roots of unity and some highest weight representations of the sl(2) loop algebra

Abstract

We discuss irreducible highest weight representations of the sl(2) loop algebra and reducible indecomposable ones in association with the sl(2) 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.

10 pages, no figures, submitted to the proceedings of the international workshop ``Recent Advances in Quantum Integrable Systems'', September 6-9, 2005, LAPTH, Annecy-le-Vieux, France

References in corpus (1)

• XXZ Bethe states as highest weight vectors of the $s{l}_2$ loop algebra at roots of unity

Cited by in corpus (4)

• Irreducibility criterion for a finite-dimensional highest weight representation of the sl(2) loop algebra and the dimensions of reducible representations
• Extension of a Borel subalgebra symmetry into the sl(2) loop algebra symmetry for the twisted XXZ spin chain at roots of unity and the Onsager algebra
• Generalized Drinfeld polynomials for highest weight vectors of the Borel subalgebra of the $s{l}_2$ loop algebra
• On the Degenerate Multiplicity of the $s{l}_2$ Loop Algebra for the 6V Transfer Matrix at Roots of Unity