# How to Decompose finite dimensional irreducible representation of $SO(d+1,1)$ into irreps of the subgroup $SO(d)\times SO(1,1)$?

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?