Author(s)

Aboubacar Nibirantiza¹, Pascal Ndayisenga²

¹Department of Mathematics, Institute for Applied Pedagogy, University of Burundi, Bujumbura, Burundi.
²Department of Mathematics, Faculty of Sciences, University of Burundi, Bujumbura, Burundi.

The research paper investigates the computation of Casimir operators on $\mathfrak{s}{\mathfrak{l}}_2$ -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 $\mathfrak{s}{\mathfrak{l}}_2$ -modules and Schur’s Lemma, enriching the understanding of their role in differential geometry and representation theory.

Module Structures, Adjointe Action of Lie Algebra, Schur Lemma, Equivalence of Representations

Nibirantiza, A. and Ndayisenga, P. (2025) Casimir Operators on the sl₂ - Modules of the Linear Differential Operators and the Associated Symbols on the Real Line. Journal of Applied Mathematics and Physics, 13, 1428-1438. doi: 10.4236/jamp.2025.134077.