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Generalized Drinfeld polynomials for highest weight vectors of the Borel subalgebra of the $sl_2$ loop algebra

Tetsuo Deguchi
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Abstract

In a Borel subalgebra U(B) of the sl(2) loop algebra, we introduce a highest weight vector $Ψ$. We call such a representation of U(B) that is generated by $Ψ$ highest weight. We define a generalization of the Drinfeld polynomial for a finite-dimensional highest weight representation of U(B). We show that every finite-dimensional highest weight representation of the Borel subalgebra is irreducible if the evaluation parameters are distinct. We also discuss the necessary and sufficient conditions for a finite-dimensional highest weight representation of U(B) to be irreducible.

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Tetsuo Deguchi. 2006-06-30. Generalized Drinfeld polynomials for highest weight vectors of the Borel subalgebra of the $sl_2$ loop algebra. https://arxiv.org/abs/math-ph/0606071

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