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arXiv · 2311.05358

The uniform structure of $\mathfrak{g}^{\otimes 4}$

Maneh Avetisyan·Alexey Isaev·Sergey Krivonos·Ruben Mkrtchyan
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Abstract

We obtain a uniform decomposition into Casimir eigenspaces (most of which are irreducible) of the fourth power of the adjoint representation $\mathfrak{g}^{\otimes 4}$ for all simple Lie algebras. We present universal, in Vogel's sense, formulae for the dimensions and split Casimir operator's eigenvalues of all terms in this decomposition. We assume that a similar uniform decomposition into Casimir eigenspaces with universal dimension formulae exists for an arbitrary power of the adjoint representations.

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Maneh Avetisyan, Alexey Isaev, Sergey Krivonos, Ruben Mkrtchyan. 2023-11-09. The uniform structure of $\mathfrak{g}^{\otimes 4}$. https://arxiv.org/abs/2311.05358

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