Projectors on invariant subspaces of representations of Lie algebras and and Vogel parameterization

• Published in: Theoretical and mathematical physics Vol. 206; no. 1; pp. 1 - 18
• Main Authors: Isaev, A. P., Provorov, A. A.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 2021; Springer Nature B.V
• Subjects: 14/34; 639/766/189; 639/766/530; 639/766/747; Algebra; Applications of Mathematics; Invariants; Lie groups; Mathematical and Computational Physics; Parameterization; Physics; Physics and Astronomy; Projectors; Representations; Subspaces; Theoretical; simple Lie algebra; Vogel parameter; split Casimir operator; projector; invariant subspace
• ISSN: 0040-5779; 1573-9333
• DOI: 10.1134/S0040577921010013

Using the split Casimir operator, we find explicit formulas for the projectors onto invariant subspaces of the
representation of the algebras
and
. We also consider these projectors from the standpoint of the universal description of complex simple Lie algebras using the Vogel parameterization.