  In 2006, Belkale and Kumar define a new product on the cohomology of flag
varieties and use this new product to give an improved solution to the
eigencone problem for complex reductive groups. In this paper, we give a
generalization of the Belkale-Kumar product to the branching Schubert calculus
setting. The study of Branching Schubert calculus attempts to understand the
induced map on cohomology of an equivariant embedding of flag varieties. The
main application of our work is a compact formulation of the solution to the
branching eigencone problem.
