Tensor operators of the Lie algebras $\mathfrak u(m)$ and $\mathfrak o(\nu)$

Computationally simple expressions are obtained for the matrix elements of the tensor operators of the Lie algebras $\mathfrak u(m)$ and $\mathfrak o(\nu)$ in bases of irreducible representations. They are obtained in the form of Bell polynomials of sums of powers of the hook lengths $p_{ij}$. Recursion relations and generating functions are also found. An example of the use of the obtained expressions in nuclear physics is given.