English

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

Mathematical Physics 2007-05-23 v1 math.MP

Abstract

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

Keywords

Cite

@article{arxiv.math-ph/0606071,
  title  = {Generalized Drinfeld polynomials for highest weight vectors of the Borel subalgebra of the $sl_2$ loop algebra},
  author = {Tetsuo Deguchi},
  journal= {arXiv preprint arXiv:math-ph/0606071},
  year   = {2007}
}

Comments

10 pages, no figure, to appear in the proceedings of the 23rd International Conference of Differential Geometric Methods in Theoretical Physics, August 20-26, 2005, Nankai Institute of Mathematics, Tianjin, China