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A recursion formula for Branching from mathfrak{sl}_n to mathfrak{sl}₂ subalgebras
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A recursion formula for Branching from mathfrak{sl}_n to mathfrak{sl}₂ subalgebras
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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.
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