I want to know how can one decompose a non-trivial finite dimensional irreducible representation (obviously not unitary) of generalized Lorentz Group like $SO(d+1,1)$ into irreducible representations of its subgroup $SO(d)\times SO(1,1)$. For example, consider the spin-2 tensor representation of $SO(d+1,1)$ ,that expressed by a Young Tableaux having a single row with two boxes, gets decomposed into the corresponding Young Tableaux representations of $SO(d)$ with associated $SO(1,1)$ charges. How can one determine this spectral decomposition?


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