1999/09/22 by V. D. Gladush, R. A. Konoplya
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Casimir effect #Casimir element #Classical mechanics #Exact solutions in general relativity #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Operator (biology) #Physics #Pure mathematics #Quantum Electrodynamics and Casimir Effect #Tensor (intrinsic definition) #Tensor field #gr-qc #math-ph #math.MP #math.RT
paper · pdf · doi:10.1063/1.533240
published as J.Math.Phys. 41 (2000), 2299-2309 · 13 pages, RevTex
arxiv created 1999/09/22 · openalex publication_date 2000/04/01 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A new method of the constructing of the basic functions for spaces of tensor representations of the Lie groups, with the help of the generalized Casimir operator, has been proposed. In the definition of the operator there we used the Lie derivatives instead of the corresponding infinitesimal operators. When introducing the generalized Casimir operator we used the metric for which a group being considered will be isometry that follows from the invariance condition for the generalized Casimir operator. This allows us to formulate the eigenvalue and eigenfunction problems correctly. The invariant projection operators have been constructed in order to separate irreducible components. The cases of the Bianchi type G3IX and G3II groups are considered as examples.