A recursion formula for Branching from \mathfraksl_n to \mathfraksl₂ subalgebras

2025/02/11 by Korkeat Korkeathikhun, Borworn Khuhirun, Korkeathikhun, Korkeat +5
Mathematics · #05E10 #17B10 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2502.19426

openalex publication_date 2025/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any representation of a complex simple Lie algebra \mathfraksl_n, one problem of branching rules to \mathfraksl₂-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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