2006/06/30 by Tetsuo Deguchi, Deguchi, Tetsuo
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0606071
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
arxiv created 2006/06/30 · openalex publication_date 2006/06/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.