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In a Borel subalgebra U(B) of the sl(2) loop algebra, we introduce a highest weight vector $\Psi$. We call such a representation of U(B) that is generated by $\Psi$ 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.

Generalized Drinfeld Polynomials for Highest Weight Vectors of the Borel Subalgebra of the sl2 Loop Algebra

Generalized Drinfeld Polynomials for Highest Weight Vectors of the Borel Subalgebra of the sl₂ Loop Algebra