TITLE: Tensoring irreducible $B$-series representations/ Type B Littlewood-Richardson
QUESTION [5 upvotes]: When tensoring finite dimensional representations of the Lie algebra ${\frak sl}_n$, we have an explicit algorithm given in terms of Young diagrams. See Section 4 of this paper.
Do there exist similar pictures for the $B$ and $D$ series? I am specifically interested in simplest case, where one of the irreducible representations being tensored is the fundamental representation.

REPLY [4 votes]: Littelmann used standard monomial theory to give a unified Littlewood–Richardson rule for the simple reductive algebraic groups of types $A$, $B$, $C$ and $D$ (and some others) in which the coefficients enumerate certain generalized standard tableaux. See (a) in the theorem on page 346 of Littlemann's paper,  A generalization of the Littlewood-Richardson rule., J. Alg. 130 (1990) 328–368.