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

Korkeat Korkeathikhun; Borworn Khuhirun; Songpon Sriwongsa; Keng Wiboonton

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arXiv · 2502.19426

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

Korkeat Korkeathikhun·Borworn Khuhirun·Songpon Sriwongsa·Keng Wiboonton

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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.

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Korkeat Korkeathikhun, Borworn Khuhirun, Songpon Sriwongsa, Keng Wiboonton. 2025-02-11. A recursion formula for Branching from $\mathfrak{sl}_n$ to $\mathfrak{sl}_2$ subalgebras. https://arxiv.org/abs/2502.19426

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