We present the implementation of the Littlewood-Richardson rule in LiE. We describe the mathematical problem it applies to, formulate the rule, and indicate a proof. In a brief historical sketch we indicate some early formulations and partial proofs. We derive a formulation of the rule that can be implemented very efficiently.

Symmetric functions and generalizations (msc 05E05), Combinatorial aspects of representation theory (msc 05E10), Explicit machine computation and programs (not the theory of computation or programming) (msc 20-04), Representations of finite symmetric groups (msc 20C30), Representation theory (msc 20G05)
Modelling, Analysis and Simulation [MAS]

van Leeuwen, M.A.A. (1997). The Littlewood-Richardson rule, theory and implementation. Modelling, Analysis and Simulation [MAS]. CWI.