Projectors on invariant subspaces of representations $\operatorname{ad}^{\otimes 2}$ of Lie algebras $so(N)$ and $sp(2r)$ and Vogel parametrization

A. A. Provorov; A. P. Isaev

Projectors on invariant subspaces of representations operatorname{ad}^(otimes 2) of Lie algebras so(N) and sp(2r) and Vogel parametrization

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arxiv 2012.00746 v2 pith:VOUUXZ6K submitted 2020-11-30 math-ph hep-thmath.MP

Projectors on invariant subspaces of representations operatorname{ad}^(otimes 2) of Lie algebras so(N) and sp(2r) and Vogel parametrization

A. P. Isaev , A. A. Provorov This is my paper

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keywords projectorsalgebrasbeeninvariantoperatornameotimessubspacesvogel

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Explicit formulae for the projectors onto invariant subspaces of the $\operatorname{ad}^{\otimes 2}$ representation of the Lie algebras $so(N)$ and $sp(2r)$ have been found by means of the split Casimir operator. These projectors have also been considered from the viewpoint of the universal complex simple Lie algebra description by using the Vogel parametrisation.

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