A recursion formula for Branching from ${\mathfrak{sl}}_n$ to ${\mathfrak{sl}}_2$ subalgebras

Abstract

For any representation of a complex simple Lie algebra ${\mathfrak{sl}}_n$, one problem of branching rules to ${\mathfrak{sl}}_2$-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.

14 pages