Let $G$ be a semisimple simply connected group over an algebraically closed field $k$, $B$ a Borel and $T$ a maximal torus. Let $\lambda,\mu,\nu$ be dominant characters of $T$. Let $V(\lambda)$ be the irreducible representation of highest weight $\lambda$.

If $\lambda=\mu+\nu$, then we know that $V(\lambda)$ is the direct factor of multiplicity one inside $V(\mu)\otimes V(\nu)$.

Is it possible to characterize $V(\lambda)$ inside this tensor product ?

Let $G$ be a semisimple simply connected group over an algebraically closed field $k$ of characteristic zero, $B$ a Borel and $T$ a maximal torus. Let $\lambda,\mu,\nu$ be dominant characters of $T$. Let $V(\lambda)$ be the irreducible representation of highest weight $\lambda$.

If $\lambda=\mu+\nu$, then we know that $V(\lambda)$ is the direct factor of multiplicity one inside $V(\mu)\otimes V(\nu)$.

Is it possible to characterize $V(\lambda)$ inside this tensor product ?