The research paper investigates the computation of Casimir operators on sl_(2)-modules associated with linear differential operators and symbols on the real line.The study considers spaces of differential operators an...The research paper investigates the computation of Casimir operators on sl_(2)-modules associated with linear differential operators and symbols on the real line.The study considers spaces of differential operators and principal symbols related to tensor densities,and derives explicit formulas for the Casimir operators.It extends previously known results about sl_(2)-modules and Schur’s Lemma,enriching the understanding of their role in differential geometry and representation theory.展开更多
文摘The research paper investigates the computation of Casimir operators on sl_(2)-modules associated with linear differential operators and symbols on the real line.The study considers spaces of differential operators and principal symbols related to tensor densities,and derives explicit formulas for the Casimir operators.It extends previously known results about sl_(2)-modules and Schur’s Lemma,enriching the understanding of their role in differential geometry and representation theory.
