Casimir operators of the exceptional group $F_4$: the chain $B_4\subset F_4\subset D_{13}$

Details Casimir operators of the exceptional group $F_4$: the chain $B_4\subset F_4\subset D_{13}$ Casimir operators of the exceptional group $F_4$: the chain $B_4\subset F_4\subset D_{13}$

1993-12-16

arxiv.org/abs/hep-th/9312148v1

J.Phys. A27 (1994) 3847-3856

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.1088/0305-4470/27/11/033

Expressions are given for the Casimir operators of the exceptional group $F_4$ in a concise form similar to that used for the classical groups. The chain $B_4\subset F_4\subset D_{13}$ is used to label the generators of $F_4$ in terms of the adjoint and spinor representations of $B_4$ and to express the 26-dimensional representation of $F_4$ in terms of the defining representation of $D_{13}$. Casimir operators of any degree are obtained and it is shown that a basis consists of the operators of degree 2, 6, 8 and 12.

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