split Casimir operator of the and simple Lie superalgebras in the representation and the Vogel parameterization

• Published in: Theoretical and mathematical physics Vol. 221; no. 1; pp. 1726 - 1743
• Main Authors: Isaev, A. P., Provorov, A. A.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 2024; Springer Nature B.V
• Subjects: 14/34; 639/766/189; 639/766/530; 639/766/747; Applications of Mathematics; Mathematical and Computational Physics; Parameterization; Physics; Physics and Astronomy; Projectors; Representations; Subspaces; Theoretical; split Casimir operator; Vogel parameters; projector; simple Lie superalgebra; invariant subspace
• ISSN: 0040-5779; 1573-9333
• DOI: 10.1134/S004057792410009X

We find universal characteristic identities for the
-split Casimir operator in the representation
of the
and
Lie superalgebras. Using these identities, we construct projectors onto the invariant subspaces of these representations and find universal formulas for their superdimensions. All the formulas are in accordance with the universal description of subrepresentations of the
representation of simple basic Lie superalgebras in terms of the Vogel parameters.