Reduction for branching multiplicities

Abstract: A reduction formula for the branching coefficients of tensor products of representations and more generally restrictions of representations of a semisimple group to a semisimple subgroup is proved in work by Knutson-Tao and Derksen-Weyman. This formula holds when the highest weights of the representations belong to a codimension 1 face of the Horn cone, which by work by Ressayre corresponds to a Littlewood-Richardson coefficient equal to 1. We prove a similar reduction formula when this coefficient is equal to 2, and show some properties of the class of the branch divisor corresponding to a generically finite morphism of degree 2 naturally defined in this context.