A recursion formula for branching from 𝔰𝔩n to 𝔰𝔩2 subalgebras

For any representation of a complex simple Lie algebra [Formula: see text], one problem of branching rules to [Formula: see text]-subalgebra is to determine the multiplicity of each irreducible component. In this paper, we derive a recursion formula of such multiplicities by restricting a certain tensor representation in two ways, in which the Pieri’s rule is involved. We also investigate branching rules for fundamental representations as they are initial conditions of the recursion formula.