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 $lambda_1geldotsgelambda_nge 0gemu_1geldotsgemu_n$ is especially interesting for me.

Any references would be appreciated.