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](http://www.phys.nthu.edu.tw/~class/group_theory2012fall/doc/tensor.pdf).


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.



Tensoring irreducible $B$-series representations/ Type B Littlewood-Richardson
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](https://core.ac.uk/download/pdf/82209803.pdf), *A generalization of the Littlewood-Richardson rule.*, J. Alg. **130** (1990) 328–368.


