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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

A. P. Isaev , A. A. Provorov This is my paper · ORCID
classification math-phhep-thmath.MP
keywords projectorsalgebrasbeeninvariantoperatornameotimessubspacesvogel
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abstract

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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Torus knots in adjoint representation and Vogel's universality

    hep-th 2025-06 conditional novelty 6.0 of 10

    Universal adjoint invariants for T[4,n] torus knots are constructed via Vogel's universality, completing the T[4,n] case after previous T[2,n] and T[3,n] results.

  2. Macdonald deformation of Vogel's universality and link hyperpolynomials

    hep-th 2025-05 conditional novelty 6.0 of 10

    For the adjoint square in ADE Lie algebras, products of Macdonald dimensions with deformed Littlewood-Richardson coefficients are universal, yielding universal formulas for T[2,2n] link hyperpolynomials.

  3. Vogel's universality and Macdonald dimensions

    hep-th 2025-07 conditional novelty 4.0 of 10

    The paper gives a single rational formula for adjoint Macdonald dimensions that unifies the simply laced Lie algebras A_n, D_n, E6, E7, E8, plus explicit mixed-root-system dimension formulas.

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