It is known that every irreducible representation of the unitary group $U(n)$ can be uniquely described by the non-increasing sequence $\lambda=(\lambda_1,\ldots,\lambda_n)$ of integers (denote the corresponding representation as $V_{\lambda}$). Does there exist a formula (like Littlewood-Richardson rule for $GL(n)$) for the decomposition of the tensor product $V_{\lambda}\otimes V_{\mu}$?

In terms of characters it means that we need to decompose the product of 'Schur functions' $s_{\lambda}s_{\mu}$ into the sum of some $s_{\nu}$ (but here $\lambda,\mu,\nu$ might have negative 'parts').

The case when $\lambda_1\ge\ldots\ge\lambda_n\ge 0\ge\mu_1\ge\ldots\ge\mu_n$ is particularly interesting for me.

Any references would be appreciated.